Compact stars admitting Finch-Skea symmetry in the presence of various matter fields*PKS acknowledges National Board for Higher Mathematics (NBHM) under Department of Atomic Energy (DAE), Govt. of India for financial support to carry out the Research project No.: 02011/3/2022 NBHM (R.P.)/R#D II/2152 Dt.14.02.2022. Sokoliuk O. performed the work in frame of the "Mathematical modeling in interdisciplinary research of processes and systems based on intelligent supercomputer, grid and cloud technologies" program of the NAS of Ukraine. (1st January 2023)