We have been developing a superconducting time-of-flight mass spectrometry (TOF-MS) system, which utilizes a superconductive strip ion detector (SSID) and a single-flux-quantum (SFQ) multi-stop time-to-digital converter (TDC). The SFQ multi-stop TDC can measure the time intervals between multiple input signals and directly convert them into binary data. In this study, we designed and implemented 24-bit SFQ multi-stop TDCs with a 3×24-bit FIFO buffer using the AIST Nb standard process (STP2), whose time resolution and dynamic range are 100ps and 1.6ms, respectively. The timing jitter of the TDC was investigated by comparing two types of TDCs: one uses an on-chip SFQ clock generator (CG) and the other uses a microwave oscillator at room temperature. We confirmed the correct operation of both TDCs and evaluated their timing jitter. The experimentally-obtained timing jitter is about 40ns and 700ps for the TDCs with and without the on-chip SFQ CG, respectively, for the measured time interval of 50µs, which linearly increases with increase of the measured time interval.