Early Church Fathers on Apostolic Succession . . .

Evangelical and Fundamentalist Christians deny the reality of Apostolic Succession, which is one of the four marks of the Church (One, Holy, Catholic, Apostolic).  By rejecting the idea that Apostolic power was handed down to successors (Bishops), they not only deny the Scriptures (Acts 1:20-26), but the beliefs of the Early Church as well.

Clement of Rome - Our Apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned, and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry (Letter to the Corinthians 44:1 [A.D. 95]).

Ignatius of Antioch - You must all follow the bishop as Jesus Christ follows the Father, and the presbytery as you would the Apostles. Reverence the deacons as you would the command of God. Let no one do anything of concern to the Church without the bishop. Let that be considered a valid Eucharist which is celebrated by the bishop, or by one whom he appoints. Wherever the bishop appears, let the people be there; just as wherever Jesus Christ is, there is the Catholic Church (Letter to the Smyrnaeans 8:1 [A.D. 110]).

Irenaeus - And we are in a position to enumerate those who were instituted bishops by the Apostles, and their successors to our own times: men who neither knew nor taught anything like these heretics rave about. For surely they wished all those and their successors to be perfect and without reproach, to whom they handed on their authority (Against Heresies 3:3:1 [A.D. 180-199]).

Tertullian - For this is the way in which the apostolic Churches transmit their lists: like the Church of the Smyrnaeans, which records that Polycarp was placed there by John; like the Church of the Romans where Clement was ordained by Peter. In just this same way the other Churches display those whom they have as sprouts from the apostolic seed, having been established in the episcopate by the Apostles. Let the heretics invent something like it. (The Demurrer Against the Heretics 32:1 [A.D. 200]).

Clement of Alexandria - After the death of the tyrant, the [Apostle John] came back again to Ephesus from the Island of Patmos; and, upon being invited, he went even to the neighboring cities of the pagans, here to appoint bishops, there to set in order whole Churches, and there to ordain to the clerical estate such as were designated by the Spirit (Who is the Rich Man that is Saved? 42:2 [inter 190-210 A.D.]).

Firmilion of Caesarea
Therefore, the power of forgiving sins was given to the Apostles and to the Churches which these men, sent by Christ, established; and to the bishops who succeeded them by being ordained in their place (Letter to Cyprian 75:16 [A.D. 255-256]).