Stepping into Specific Function in GDB

Does GDB support Stepping into a Specific function

No. If you want to step into g, a simple step should do it. If you want to step into f, do step, finish, step.

You are welcome to file a feature request in GDB bugzilla, though I doubt Step into Specific can be reasonably implemented in a CLI debugger.

The command advance from the answer https://stackoverflow.com/a/1133403/2708138 is useful. You can combine that command with print f to get the type of f in the current context beforehand.

Furthermore, I have already mentioned in the comment to your question that you can skip the function g if you never want to step through it.

See the gdb-help for the keywords advance, print and skip.

At least the skip-feature is quite new. So maybe, it was not available at the time when Employed Russian gave his answer.