Auxiliary power supply (APS) is an essential component of medium voltage (MV) solid state transformers (SSTs) feeding the auxiliary units, such as gate drivers, controllers and sensors. Usually APSs are obtained from the distributed bus, which may cause the input voltage imbalance before the main power transmission. This paper proposed a new design for isolated APS of an input-series output-parallel (ISOP) SST. The designed distributed MV APSs are galvanically isolated by flybacks, and the centralized APS on the low voltage (LV) side is supplied from the MV APSs via a decoupling four-port medium frequency transformer (MFT) with high isolation voltage. To solve the issue of input voltage imbalance posed by the ISOP system, a dual-loop control scheme based on APS-fluctuating is proposed, which can realize output voltage regulation (OVR) and input voltage sharing (IVS) simultaneously. The small-signal model, start-up strategy and parameter design of the proposed system are investigated. Finally, a 500 V/2.2 kW lab prototype of SST with APS has been built and the overall system efficiency reaches 95.1%.