Which will be the next digit in series 3968 63 8 3?

2

Add 1 to the number and then take the square root.

3968 + 1 = 3969 : √3969 = 63

63 + 1 = 64 : √64 = 8

8 + 1 = 9 : √9 = 3

3 + 1 = 4 : √4 = 2.