I doubt that you need to do anything at all that you wouldn't do for any other paper. I think self-citation is really only an issue when it is overdone and/or no one else agrees with you. 

But if they (hopefully) believe what you are writing at present, they don't need to be "warned" that you also wrote something similar or supporting in the past. 

If you normally say "Smith in [3] says,..." and you are Jones, then you can say "Jones in [5] implies..." or similar. There are other answer/comments here that give other suggestions if you really think you need to be more specific.