Two points to note:

1.  "Verify" or "determine"?

I agree with James's answer (we need to use "the") and note that he was careful to include "claimed" in the example he gave.  In general, if efficacy has been claimed or asserted in a report, we VERIFY the report/claim/efficacy.  If it is virgin territory (i.e. no one has issued a report or made a claim), we use the verb DETERMINE.  Example:  Clinical trials are used to determine the efficacy of a drug.

2.  "Efficacy" or "effectiveness"?

"Efficacy" refers solely to whether a drug can treat the condition it is intended for and (deliberately) disregards its tolerability (side effects, toxicity, etc) and ease of use.  "Effectiveness" takes efficacy, tolerability and ease of use into account.  Example:  Observational studies (not clinical trials) are used to determine the effectiveness of a drug.

Please note these distinctions so that you may choose the right verb and the right noun to use.

Please remember always to quote a full sentence or paragraph in future if you wish to see a full answer that takes context into consideration.  You will get better answers and learn more that way.

Is it correct to say "verifying efficacy of drugs"?

verify the efficacy

The purpose of the study was to verify the efficacy of the drug as claimed by the manufacturer.