For the purpose of claiming salry, evidence of your duty and official relieving by the company after your resignation is more important, rather than your appointment letter/ employment.
In fact, your questions are quite vague, like "company not given any appointment letter then how can they ask 1 month notice peroid," and."after submission my resign letter i worked 18 days then i left in my person problem then how can they hold my PL and 18 days worked salary."
If they have asked for resignation notice that clearly means the company does not want to violate service laws of the land. I you don't know the provisions of law that does not mean that the campmny cannot ask you to submit your resignation with one month notice.
Secondly, if you unauthorisedly absented at your own due to your own personal problem without expirey of notice period, that also not absolves you not to obtain NOC from different departments/ branches about no liability against you before the company settles your full & final.
Instead of raining vague questions, you could rather have contacted the HR department of your company to complete the formalities of your regular relief. However, nobody can debar you from legally fighting againist the company, if you can prove your own actions to be legal. Once you get any employment, you are also under obligation to observe the provisions of service laws to establish your rightful claims.