Working in Zurich for the part 1.5 years.Planning to move to Basel by end of July.
Currently with L permit.New employer is ready to apply for B Permit.
Is it possible to get B permit in Basel?what is the chances for this?

I am a Non EU.Working as a contract employee in Zurich.
The new employer is a local company.

1. Your employer does not apply for a permit type - the authorities decide on which type to issue.

2. Changing employers on an L permit is not normally allowed in country - it can be done under exceptional circumstances but your situation does not sound like one of them.

3. To do what you want probably requires you to leave the country for a few months or even up to a year.