Evidential Apologetics is that style of Christian defense that stresses the miracles found in the Bible, particularly Christ's resurrection, as an evidence for the existence of God and the validity of Christ and His words. It also uses historical evidences to support the veracity of the biblical account(s). In this, it is very similar to Classical Apologetics which stresses reason in its approach to evidences. Basically, evidential apologetics stresses evidence such as miracles, fulfilled prophecies, etc. and uses reason to support them.
An example of evidential apologetics might be as follows (Note the similar argument to the classical approach):
Allen: How do I know God exists?
Paul: One of the ways can be found in the gospel accounts where Jesus performed many miracles like walking on water, healing the sick, etc. and then finally rising from the dead. No mere man can do those kinds of things. There had to be something supernatural at work. Why can't that be God?
Allen: But the Bible is full of myths. It is just a bunch of stories.
Paul: Actually, they are not just myths and stories. The gospels, for example, were written by those who either knew Jesus personally, or were under the direction of those who did. The gospels are full of factual accounts of cities, customs, terms, locations, etc., that can all be verified historically and archaeologically. There are many books that have verified the authenticity of the gospel accounts.
Allen: If that is true, then I am sure the gospels have been corrupted over time.
Paul: Actually, that isn't quite accurate. You see, the New Testament alone has something like 24,000 supporting biblical manuscripts and they are around 99.5% textually pure. That means that they have been reliably transmitted to us through the centuries. We can trust them.
Allen: Still, I can't believe all those miracles and stuff.
Paul: Why not? Many eyewitnesses wrote and spoke about what they saw Jesus do. After the gospel accounts were written, there were plenty of people around who had seen Jesus who could have spoken up or written something down contradicting what the apostles wrote. But, we have no account of this happening.
Allen: I didn't think of that.
Paul: Furthermore, since the eyewitnesses wrote about what they saw, and they saw miracles, as did hundreds of others, and Jesus healed people, walked on water, calmed a storm by a command, and rose from the dead, then whatever He says must be true since He backed up His words with His deeds.
Allen: That makes sense, but that doesn't mean there is a God.
Paul: True, it doesn't require that a God exist, but since Jesus spoke about God, about the need to be right with God, etc., and since He performed many miracles including rising from the dead, then it is safe to say that not only is there a God, but that we should listen to Jesus. This would also mean that the Bible is the inspired word of God.
Allen: I'll have to think about what you said.
Generally, the evidential apologetics stresses data that supports the miraculous evidences of the biblical accounts thereby authenticating the Bible and the claims and deeds of Jesus.
Adherents to this position have been B. B. Warfield, John Warwick Montgomery, Clark Pinnock, etc.