Andhra Pradesh Open School Society is an autonomous society that has been registered under the AP Public Societies act and is recognised by the Government of AP. So if you have completed your 12th from APOSS it is valid for appearing for NEET, TS and AP EAMCET. A look at the eligibility criteria will help you understand that:

NEET: You should have completed your 12th from any recognised Institution. And to be eligible for NEET, you should have completed your 12th, passed in all subjects and secure a minimum aggregate of 50% in Physics, Chemistry and Biology. It is 50% for General Category, 45% for PWD and 40% for OBC,SC,ST. Now if you belong to OBC Category, the Category you belong to should be also listed in the Central OBC list. Or else you will be considered as General Category and so you have to secure a minimum aggregate of 50% in Physics, Chemistry and Biology. This 50% is inclusive of the Theory and Practical marks scored in Physics, Chemistry and Biology collectively. You needn't score 50% in Physics, 50% in Chemistry and 50% in Biology separately. You need an aggregate of 50% or 40% depending on your Category as an aggregate in Physics, Chemistry and Biology. And along with Physics, Chemistry and Biology, you should also have studied English as one of the core subjects in your 12th.

TS and AP EAMCET: You should belong to AP or Telangana and should have completed your 12th or equivalent examination from the the Board of Intermediate Education of Telangana or AP. If you look at the Information Brochure, APOSS is a recognised University to study your 10th and 12th from and then be eligible for TS and AP EAMCET.