The solution is as follows

Case 1: Generally, in these cases, the HR Manager of the prospective employer would generally ask for the resignation letter you have submitted, the communication you had with your current employer and their willingness to relieve you after 3 months.

By providing this information, the prospective employer mostly accepts you into their organization. Open up the communication and see the results

Case 2: Explain the current employer that you would help them in completing the project by working on weekends and ask for the relieving letter

Take the above 2 chances. Hope for the best.