We study the AdS/CFT correspondence by using the Schur index, which is the special limit of the superconformal index. Most of this talk, we focus on the correspondence between 4d N=4 U(N) SYM and Type IIB superstring theory on AdS_5×S^5. The agreement of the index at large N limit has confirmed by Kinney et al., but the case of finite N was a long mystery for last decade. In this talk, we propose a calculation method of the index on AdS side for finite N. The key point is to consider D3-branes wrapping three-cycles in S^5. We explicitly calculate contributions of these wrapping D3-branes to the index by analyzing fluctuations on the D3-branes. As far as we checked numerically, our results correctly reproduce the index on CFT side. We also try to apply our method to 4d S-fold theories, which are generalizations of the orientifold theories and have N=3 supersymmetry. Since it is known that S-fold theories have no Lagrangian description, we have to calculate the index on AdS side based on AdS/CFT correspondence. For some special cases, the supersymmetry is enhanced to N=4, and we use this phenomenon as a check for our prediction. You can also see our results are consistent with the supersymmetry enhancement.