Which sentence is correct? Or are both sentences correct?

1. However sincerely he worked, he wasn’t given promotion.
2. Sincerely as he worked, he wasn’t given promotion.

Both sentences are correct.
 

1. However sincerely he worked, he wasn’t given promotion.
2. Sincerely as he worked, he wasn’t given promotion.

 
Depending on the situation, it might be better and sound more natural if you use a different adjective other than sincerely. Such as: honestly, genuinely, diligently, tirelessly, painstakingly, enthusiastically. 
 
For example:

• However genuinely he worked, he wasn’t given promotion.
• However tirelessly he worked, he wasn’t given promotion.
• Enthusiastically as he worked, he wasn’t given promotion.
• Honestly as he worked, he wasn’t given promotion.