In the study of Kahler-Einstein problem on Fano manifolds, we consider a general continuity path mixed with conical singularities along a simple normal crossing divisor and
a twisted positive form. We can show the partial C^0-estimate along such a general continuity path, which generalizes the result along the path of conical Kahler-Einstein metrics and Aubin's classical path. As a conclusion, we could show the Yau-Tian-Donaldson conjecture in a new situation. This work is joint with Ke Feng.