Is there any indemnity if an employee works for 11 months in the company in Bahrain?

There is no minimum period required to be entitled to leaving indemnity.

Generally, it is due to foreign employees (non-Bahrainis) and will be calculated based on the period of service.

But if you work for less than a year, the amount you will get will be limited to less than half a month's salary.

Yes, there is a leaving indemnity which is calculated pro-rata based on the term of employment.