Not a blind bit/the blindest bit of…
Definition 1 of 1
Pro Tip 1/3British Idiom
Used mainly in British English, not common in American or other English variants. 
He tried to impress her, but it didn't make a blind bit of difference.
Pro Tip 2/3Strong Negation
Emphasizes a complete lack of impact or concern; stronger than saying 'not much' or 'little'. 
The criticism didn't make a blind bit of difference to her decision.
Pro Tip 3/3Emotional Dismissal
Often shows emotional disregard or indifference when used in personal contexts. 
I don't give a blind bit about those rumors.