Absconding - join another company without mentioning my experience?

I have left a company after completing one month. Draft a formal resignation letter. Haven't signed any offer or appointment letter so no question of serving notice period. Can I join another company by submitting my previous company payslip and relieving letter without mentioning my experience in these company??

It doesn't appear that you require any assistance to draft a resignation letter. As regards your effort to conceal your current employment, it is a risk you are carrying and is also unethical. As you are going for formal resignation, what stops you from taking due credit for it remains an enigma.