Church Authority from a few scripture verses:

And his gifts were that some should be apostles, some prophets, some evangelists, some pastors and teachers, to equip the saints for the work of ministry, for building up the body of Christ.” (Eph 4:11-12)  Paul says:  “Now I rejoice in my sufferings for your sake, and in my flesh I complete what is lacking in Christ's afflictions for the sake of his body, that is, the church,”  (Col 1:24)  Christ’s body is his Church.  From the Bible it is clear that the one true Church is made up of prophets, evangelists, pastors (priests), and teachers, but who will lead them?  The Bible alone?  No the Church!!  “If I am delayed, you may know how one ought to behave in the household of God which is the church of the living God, the pillar and bulwark of the truth”. (1 Tim 3:15)  This is why we have the Pope, our bishops, priests, deacons, lay teachers, and etc. who follow the traditions which the Church received from Christ and has taught for the last 2000 years. "So then, brethren, stand firm and hold to the traditions which you were taught by us, either by word of mouth (oral tradition) or by letter (scripture)" (2 Thess. 2:15). We as Catholics have the full word of God in
Sacred Scripture and oral tradition!  "You, then, my son, be strong in the grace that is in Christ Jesus, and what you have heard from me before many witnesses entrust to faithful men who will be able to teach others also" (2 Tim. 2:1-2).

Biblical evidence for the Papacy & Peter as the first Pope:

"And he called to him his twelve disciples and gave them authority over unclean spirits, to cast them out, and to heal every disease and every infirmity. The names of the twelve apostles are these: first, Simon, who is called Peter . . ." (Matt. 10:1-2).  Peter is named first among the apostles.

“For even if I boast somewhat more about our authority, which the Lord has given for your upbuilding, and not for your destruction, I shall not be put to shame.”  (2Cor 10:8)

"And I tell you, you are Peter, and on this rock I will build my Church, and the powers of death shall not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth shall be bound in heaven, and whatever you loose on earth shall be loosed in heaven’" (Matt. 16:18-19).

“Simon, Simon, behold Satan has demanded to have you, that he might sift you like wheat, but I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren’” (Luke 22:31-32).

"He brought him to Jesus. Jesus looked at him, and said, ‘So you are Simon the son of John? You shall be called Cephas’ (which means Peter the Rock)" (John 1:42).  When God changes a person's name in scripture, He is giving them authority.  (Abram to Abraham, Jacob to Israel, Eliakim to Jehoiakim, Saul
to Paul, and etc.)  

“I appeal to you, brethren, to take note of those who create dissensions and difficulties, in opposition to the doctrine which you have been taught; avoid them.  For such persons do not serve our Lord Christ, but their own appetites, and by fair and flattering words they deceive the hearts of the simple-minded.”  (Romans 16:17-18)

“And after there had been much debate, Peter rose and said to them, "Brethren, you know that in the early days God made choice among you, that by my mouth the Gentiles should hear the word of the gospel and believe.” (Acts 15:7)  Peter shows his authority.

“And they rose that same hour and returned to Jerusalem; and they found the eleven gathered together and those who were with them, who said, "The Lord has risen indeed, and has appeared to Simon!" Then they told what had happened on the road, and how he was known to them in the breaking of the bread."(Luke 24:33- 36) Jesus appeared to Peter first before the other apostles.

“And he (an angel of the Lord) said to them, "Do not be amazed; you seek Jesus of Nazareth, who was crucified. He has risen, he is not here; see the place where they laid But go, tell his disciples and Peter that he is going before you to Galilee; there you will see him, as he told you." (Mark 16:6-7)  The angel specifically mentions Peter above all the other disciples.

Paul Says:  “For I am the least of the apostles, unfit to be called an apostle, because I persecuted the church of God.”  (1 Cor 15:9) Paul points out that he is not as great as the other apostles.  He does not claim more authority than Peter.  Some protestants also claim that Paul was greater than Peter because he wrote more of the New Testament than Peter.  Keep in mind that Jesus did not personally write any book in the Bible, but no one questions His authority!

“When they had finished breakfast, Jesus said to Simon Peter, ‘Simon, son of John, do you love me more than these?’ He said to him, ‘Yes, Lord; you know that I love you.’ He said to him, ‘Feed my lambs.’ A second time he said to him, ‘Simon, son of John, do you love me?’ He said to him, ‘Yes, Lord; you know that I love you.’ He said to him, ‘Tend my sheep.’ He said to him the third time, ‘Simon, son of John, do you love me?’ Peter was grieved because he said to him the third time, ‘Do you love me?’ And he said to him, ‘Lord, you know that I love you.’ Jesus said to him, ‘Feed my sheep.” (John 21:15-17).  Jesus says this three times to Peter.  The number three is used throughout Scripture for important events. (Peter denied Jesus three times, Jesus rose on the third day, Christ rebuilt the temple in three days, Jesus fell three times carrying the cross, Jesus hung on the cross for three hours, Christ dies on the cross at three, Jesus rose on the third day, the Trinity, Paul was blind for three days, and etc.).

The names of Peter, which include Simon and Cephas, are mentioned more times in the New Testament than any other Apostle.  "Of Peter the most is known. Peter is mentioned 195 times, the rest of the other Apostles combined are only 130 times. The one mentioned next in frequency to Peter is John, to whom there are 29 references."  Archbishop Fulton J. Sheen, "Life of Christ", page 106.

Apostolistic Succession:
“So then you are no longer strangers and sojourners, but you are fellow citizens with the saints and members of the household of God, built upon the foundation of the apostles and prophet, Christ Jesus himself being the cornerstone, (Eph 2:19-20) Apostolic Succession is a sign of the one true Church.

“...that you should set right anything that is defective and should appoint presbyters (priests) in every city as I myself directed you to do,”   (Titus 1:5)

“Take heed to yourselves and to the whole flock in which the Holy Spirit has placed you as Bishops to rule the Church of God,” (Acts 20:28)

“Obey your superiors and be subject to them, for they keep watch as having to render an account of your souls” (Heb 13:17)

"He who hears you, hears Me; and he who rejects you, rejects Me; and he who rejects Me, rejects Him who sent Me."  (Luke 10:16)

Peter’s shows his authority as he appoints another to take Judas’s place. “In those days Peter stood up among the brethren (the company of persons was in all about a hundred and twenty), and said, "Brethren, the scripture had to be fulfilled, which the Holy Spirit spoke beforehand by the mouth of David, concerning Judas who was guide to those who arrested Jesus. For he was numbered among us, and was allotted his share in this ministry.  ........And they put forward two, Joseph called Barsab'bas, who was surnamed Justus, and Matthias and they prayed and said, "Lord, who knowest the hearts of all men, show which one of these two thou hast chosen to take the place in this ministry and apostleship from which Judas turned aside, to go to his own place."
And they cast lots for them, and the lot fell on Matthias; and he was enrolled with the eleven apostles.” (Acts 1:16-25)  The Church is Apostolic and continued to be so even after the death of the original apostles.

"And Jesus came and said to them, "All authority in heaven and on earth has been given to me. Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you; and lo, I am with you always, to the close of the age.”  (Matt 28:18-20) The Church which Christ founded is Apostolic and will always be around until the end!

Apostolic Authority:

 

“I thank him who has given me strength for this, Christ Jesus our Lord, because he judged me faithful by appointing me to his service,”  (1Tim1:12)  Paul uses language which shows that his authority was given to him through an appointment.

“I have written something to the church; but Diot'rephes, who likes to put himself first, does not acknowledge my authority.”  (3 John 1:9)

Yes, brother, I want some benefit from you in the Lord. Refresh my heart in Christ. Confident of your obedience, I write to you, knowing that you will do even more than I say.  (Philemon1: 20-21)  Philemon has obedience to Paul even though Paul was not one if the original apostles.  

“ but just as we have been approved by God to be entrusted with the gospel, so we speak, not to please men, but to please God who tests our hearts. (1Thes 2:4)

"On arriving at Jerusalem they were welcomed by the Church and the Apostles and Presbyters (priests), and they proclaimed all that GOD had done with them." (Acts 15:4)

"Then the Apostles and the Presbyters (priests) with the whole Church decided to select representatives and to send them to Antioch with Paul and Barnabas. (Acts 15:22)

"You, then, my son, be strong in the grace that is in Christ Jesus, and what you have heard from me before many witnesses entrust to faithful men who will be able to teach others also" (2 Tim. 2:1-2).  Paul speaking to Timothy

“Hence I remind you to rekindle the gift of God that is within you through the laying on of my hands;”  (2Tim 1:6)  Paul speaking to Timothy

“For every high priest chosen from among men is appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for sins. ................. So also Christ did not exalt himself to be made a high priest, but was appointed by him who said to him, "Thou art my Son, today I have begotten thee"; as he says also in another place, "Thou art a priest for ever, after the order of Melchiz'edek."”  (Heb 5:1-6)  Priests are appointed.  We are not all appointed priests as some non-catholic Christians think.  

“And the twelve summoned the body of the disciples and said, "It is not right that we should give up preaching the word of God to serve tables. Therefore, brethren, pick out from among you seven men of good repute, full of the Spirit and of wisdom, whom we may appoint to this duty. .....................These they set before the apostles, and they prayed and laid their hands upon them.  And the word of God increased; and the number of the disciples multiplied greatly in Jerusalem, and a great many of the priests were obedient to the faith.”  (Acts 6:2-7)

“And when they had ordained to them priests in every church, and had prayed with fasting, they commended them to the Lord, in whom they believed” (Acts 14:22)

“And when they were come, and had assembled the church, they related what great things God had done with them, and how he had opened the door of faith to the Gentiles”  (Acts 14:26)

Authority through sheep:

“ This figure Jesus used with them, but they did not understand what he was saying to them.   So Jesus again said to them, "Truly, truly, I say to you, I am the door of the sheep…….  I am the good shepherd; I know my own
and my own know me, as the Father knows me and I know the Father; and I lay down my life for the sheep.” (John 10:6-15)  Jesus is the Sheppard of his sheep and later gives authority to Peter and to his 12 apostles to teach and spread his message.

“When they had finished breakfast, Jesus said to Simon Peter.....................‘Do you love me?’ And he said to him, ‘Lord, you know that I love you.’ Jesus said to him, ‘Feed my sheep.” (John 21:15-17).  Jesus tells Peter alone to feed his sheep.

“These twelve Jesus sent out, charging them, "Go nowhere among the Gentiles, and enter no town of the Samaritans, but go rather to the lost sheep of the house of Israel.” (Matt 10:5-6) Jesus told his 12 apostles to go to the lost sheep of Israel.

"Behold, I send you out as sheep in the midst of wolves; so be wise as serpents and innocent as doves..........for it is not you who speak, but the Spirit of your Father speaking through you. (Matt 10:16-20)  Jesus is not speaking to a large crowd (see Matt 10:1) of believers, but only to his 12 apostles.  He calls them all sheep and later tells Peter to feed or guide my sheep (see John 21:15-17 above).

Something to think about:

Most if not all protestant denominations retain some sort of authority over their specific doctrines and practices through church elders, councils, or through the personal opinions of its members.  Are these doctrines biblical and how do these churches know they are teaching the truth?