Field-programmable gate arrays (FPGAs) provide a significantly cheaper solution for various applications in traditional semiconductor electronics. Single flux quantum (SFQ) technologies are developing rapidly and the availability of SFQ-specific FPGA will be very useful. Towards developing such an SFQ-specific FPGA, new designs of FPGA subcircuits for both synchronous and asynchronous operation of SFQ circuits are presented in this paper. Magnetic Josephson junctions (MJJs) are used as bias limiting junctions in energy-efficient rapid SFQ (ERSFQ) biasing to implement programmable switches in various subcircuits of the proposed FPGA fabric. Designs of all FPGA subcircuits are developed and are verified through circuit simulation. Verilog hardware description language (HDL) models are also developed for all FPGA circuit blocks to facilitate large-scale FPGA simulations for the implementation of the desired circuit on the proposed FPGA fabric. Designs of a few subcircuits with switches based on nondestructive readout cell are also given in the current paper for better comparison with MJJ switch based counterparts. Programming of MJJ-based switches is based on the ability to control the critical current of MJJs externally. Recent implementations of SFQ decoder is proposed for accessing individual MJJs through the current lines in a crossbar structure. Estimations for the area and power consumption are much better in comparison to previous attempts at designing an SFQ specific FPGA.