After the signed new offer later with my new...

 This overstay is the employer's fault, so you shall file a complaint at the Labor Office, then you shall go to the Immigration and Passport Department and submit a complaint with a copy of the complaint filed against the employer.
NOTE:
If the person exceeds the length of stay specified in the visa, it is considered a violation and fines are imposed by the competent authorities in the United Arab Emirates. These fines shall be distributed as follows:
1) AED 200 on the first day,
2) AED 100 for each subsequent day.
These fees shall be paid in 1) offices of the Directorate General for Residency and Foreigners Affairs,
2) or at the airport's immigration and passport offices, plus an extra charge of AED 100 upon departure.