I have some doubts regarding Unix programming, and I didn't find any particular tag to ask Unix-based questions on Stack Overflow.
Can anyone suggest to me where I can ask questions regarding Unix-based programming?
You can ask any type of programming-related question on Stack Overflow. It isn't limited to any specific type of programming questions.
As to why you didn't find any tags relating to Unix programming, I suspect that's because for the majority of questions, the particular operating system in use is irrelevant. The most important thing to tag your questions with is the language that you're using, not the operating system. For example, you can write C++ programs in Windows and Unix; both would still be tagged c++.
However, you may also be interested in the Unix/Linux Stack Exchange site. It's not necessarily intended for programming-related questions, but rather general questions about the use and abuse of Linux, BSD, and other Unix-like operating systems. From the FAQ:
Note that shell scripting is very much on-topic there (as well as on Stack Overflow), so that's something to consider if you'd prefer to target your questions to a Unix-focused audience.