Continuationism is the belief that the supernatural gifts of the Holy Spirit taught in the bible — such as prophecy, tongues, interpretation of tongues, healings, miracles, etc. — have not ceased and are available for the believer today (1 Cor. 1:7). Continuationism is the opposite of Cessationism which teaches that supernatural gifts have ceased either when the canon of Scripture was completed or at the death of the last apostle. Those who hold to continuationism are called continuationists or non-cessationists.
Cessationism, in Christian theology, is the view that the miraculous gifts of the Spirit, such as healing, tongues, and prophetic revelation, pertained to the apostolic era only, served a purpose that was unique to establishing the early church, and passed away before the canon of Scripture was closed (comp. 1 Cor. 13:8-12 with Heb. 2:3-4). It is contrasted with continuationism, which is the view that the miraculous gifts are normative, have not ceased, and are available for the believer today.
Evidentialism is a theory of justification according to which the justification of a belief depends solely on the evidence for it. Technically, though belief is typically the primary object of concern, evidentialism can be applied to doxastic attitudes generally. Formulating evidentialism in terms of the doxastic attitude of belief its most-defended form comes from Conee and Feldman: Belief, B, toward proposition, p, is epistemically justified for Subject, S, at time, t, if and only if B fits the evidence which S has at t.