In this paper, we employ the extended variable-coefficient homogeneous balance method (EvcHB), the Painlev,-Backlund transformation and the simplified Hirota's method to derive auto-Backlund transformation, multiple soliton solutions and multiple singular soliton solutions of the (3+1)-dimensional potential-YTSF equation. We also obtain a variety of traveling wave solutions, soliton-type solutions and rational solutions of distinct physical structures.