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It is usually either silk screened (the old and inaccurate way) or photolitographically made (the more modern way). The latter is often called "wet film" -- while there is another version called "dry film" (which produces thicker layers)
In any case, the process is not very hobby friendly. However, there is another kind of "paint" -- it is NOT a solder mask, but a protective lacquer which one can solder thrugh. It is used sometimes to protect the copper for oxidization, and is quite hobby-friendly stuff.
I would advice you to look for suppliers of PCB materials. For hobby stuff, the local electronics catalog sales companies often have the protective and solderable lacquer available. The real solder masks are likely not easily available to hobbyists due to more complex processes and often large containers to buy the stuff in.
what's your reason to use (as hobbist?) the soldermask? - To protect your
traces from unwanted views or to protect the copper-traces from oxidation?
In the second case it's easier to make a silver or tin-coating over them!