(a) He refused doing that.
(b) He denied doing that.
“He denied doing that” is the correct sentence as the verb to deny is usually followed by a gerund form of a verb.
Whereas the verb to refuse should be followed by an infinitive. Therefore the correct sentence for A would be “He refused to do that”.
Here are some more examples of the two verbs:
- They denied being at the restaurant that night.
- The business man denied laundering money.
- The teenagers denied stealing clothes from the mall.
- I refused to tip the waiter as he was very rude and unprofessional.
- During the three day strike the employees refused to work overtime.
- He refused to answer the police officers number and asked for a lawyer.