Is there any chance to get admission in any private medical college in MBBS in Punjab if the NEET score is 304

You havent mentioned your Category. Neverthless, in 2018, under State Quota, the cut offs for various Categories have been as follows:

General Category: 518
OBC: 470
SC: 353

Going by the previois cut offs, 304 marks is a difficult score for a Government Medical College. But you can get Private Dental College.  Having said that, cut offs change every year and are dependant on various factors like no.of seats available, no.of candidates appearing for the exam, top NEET score and difficulty of the exam. You can also check the cut offs of various different colleges under your Category at:
https://medicine.careers360.com/articles/neet-cutoff-punjab