One possibility would be the simple

asc["A"]["a"] = 99;

To change several keys:

asc[[1]][[2 ;; 3]] = 4

One possibility would be the simple

asc["A"]["a"] = 99;

As @m_goldberg commented this can be shortened to

asc["A", "a"] = 99;

To change several keys:

asc[[1]][[2 ;; 3]] = 4

One possibility would be the simple

asc["A"]["a"] = 99;

One possibility would be the simple

asc["A"]["a"] = 99;

To change several keys:

asc[[1]][[2 ;; 3]] = 4