Can I leave company without notice period in Probation period ?

My company at Bangalore provided me an offer letter via mail on 8th Jan 2022 and still now I have not received appointment letter. Few highlight points mentioned in offer letter: "This position will be on contract for a period of minimum 6 months from the date of Joining. Employment will be renewed after completion of 1 year term. Notice period while relieving will be 90 days from the date of resignation acceptance. Please sign and return duplicate copy of this letter in token of your acceptance." I have not submitted the signed copy of this offer letter. Still now, 2 months salary is pending. There is always salary delay (no proper date of salary), not received a single amount of PF and no insurance also. I felt hectic with this company. So I started searching outside job and finally got. I decided to join immediately in the new offer. On 27th April 2022, I have sent resignation mentioning about my new offer and they replied : "We accepted your resignation from the date of 27th according to your resignation mail, according to HR policies Three months is the notice period, We will try to relieve you within that possible time." Kindly suggest me in this regard. I have no time to wait. Need immediate assistance.