How to apply for a patent for original songs?

Songs cannot be patented, but they can be protected by copyright law.

Patents protect inventions, utility models and designs, and literary and artistic works are not their objects.

Generally speaking, copyright arises naturally when a work is published, and no special registration and confirmation are required. However, if you identify yourself as the copyright owner in order to provide favorable evidence in infringement disputes in the future, I suggest you register with the Copyright Bureau as soon as possible.