Which one set of letters when sequentially placed at the gaps in the given letter series shall complete it? 

a_d_an_n_ma_a_dm_n

The logic followed here is:

Given Sequence: a_d_an_n_ma_a_dm_n

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) mnadmna → amdnan / andmam / andman

Option 2) nmaadna → andman / anamad / andman

Option 3) nmadnan → andman / andman / aadmnn

Option 4) nmadnna → andman / andman / andman

Here, 'Option 4' followed a pattern.

Hence, the correct answer is "Option 4".