I can issue my own tokens via cleos, it works fine. But I can't find any reference on how to issue tokens via EOS API. Is there any way? Thanks in advance.
When you issue tokens via Cleos it creates, signs and sends a transaction containing the necessary data to call the issue-action of the token smart contract.
If you want to do the same via API (assuming via RPC-API), you need to create, sign and push a transaction containing similar data. Libraries to do so are for example EOS-JS and EOS-SHARP they also contain documentation and examples.