The magnetic flux noise caused by surface spin fluctuations in superconducting quantum interference devices (SQUIDs) limits their development. In this work, we report that different adsorbents such as H, O2, NO, and NO2 that adsorb on the surfaces of Mg-based and Pb-based SQUIDs, respectively, producing large local magnetic moments ranging from 0.7-1.6 μB, with energy barriers for thermal spin fluctuation as low as 10-30 mK. Moreover, we observe that the presence of H atoms on the surface of MgO can cause the coadsorption of other molecules, which generates additional spin sources. Monte Carlo simulations of the weakly coupled spin on a two-dimensional square lattice produce a low-frequency flux noise spectrum. We suggest eliminating the surface magnetism by coating the surface with monolayer indium phosphide or protecting the surface from other molecules by nonmagnetic preoccupants with a larger adsorption energy. The work provides important physical insights and feasible strategies for reducing magnetic noise sources in superconducting circuits.