I am a contractor that signed a contract to perform specific work for a homeowner, he argues with me about the draw payment, and then he cancels the contract after the work has been started and all the subcontractors signed contracts as well to work on the project
Generally speaking, yes. If you have performed work, and if you have not been paid for that work, you can file a lien against the project property. Your lien should not cover the entire amount of the contract, since all of the work is not complete, but it should cover the work performed, plus any other costs that may be included according to the contract.