My employer applied for an H1b petition for me this year. They notified me that they received my package back and my application is not selected in lottery. I wanted to make sure he is not lying, so I asked them for the returned package. They sent me one scanned page which has a general text which says that USCIS reieved your application but you were not selected in lottery. But nothing in that letter confirms that this H1b was filed for me only.

This page has only a FileNo: which is blank and a FormNo: which has I-129 written by hand. Is the I-129 form returned by USCIS just one page letter with no detailas about the applicant? There must be some way to associate it to an applicant?

Please advice, what document should I ask my employer to share in order to confirm that my H1b was actually filed

Why do you doubt they filed it, and to be honest, what would you do if they did not ?
The lottery is just that, only a number are selected, If you do not trust this company, then you need to find a new company for next time. Why would they not submit, if they wanted to hire you, why go to all the trouble, of application process if they were not.

Actually, they messed up a business visa that I had when I visited US. They made me stay for 5 months despite my request to return back. US embassy revoked my visa. When I wanted an explanation from my company, they mentioned they have an opening for H1B visa. I have mentoined details here

https://www.askmehelpdesk.com/immigration-law/visa-revoked-what-options-752062.html#post3477322

Please let me know in case you can advice me what document should I ask my employer to share in order to confirm that my H1b was actually filed