This is what USCIS has to say on expedition of AP: https://www.uscis.gov/forms/expedite-criteria. It specifically mentions that the "The burden is on the applicant or petitioner to demonstrate that one or more of the e​xpedite criteria have been met.​​"

That means any official document that supports your case for expedition of AP will be taken into consideration. Of course, you will need your TPS letter of approval, EAD (if you have one) and any other documentation that you think is relevant.