The format of the base URL for Modrinth's API is
branch is the branch of Modrinth you're using and
version is the version of the API you are using (the latest version of which is v2). You can learn more about how Modrinth's API versions work here.
Version 1 of the API is the only exception to this rule, as it was the following:
Version 1 is deprecated, and anything using it should be migrated to version 2. See its migration guide here.
The branch can either be
staging or nothing (production). If you're using the production server, the path will be
https://api.modrinth.com/.... These use separate databases, with
staging being primarily for testing the API before it is rolled out onto the production servers. Production uses the latest tagged on the labrinth repository, whereas
staging uses its latest commit.