How to select in the following way?

Question

Consider the following nested list:

fff = {{1, 2, {{1, 2}, {3, 4}, {19, 20}, {21, 22}}}, {2, 
   8, {{0.5, 3}, {1.4, 2}, {3, 13}, {2, 18}, {0.3, 19}, {20, 21}}}}

Each of the entries in list has the form:

{a,b,table}

I would like to remove table rows for which the first element is > 3, i.e. to obtain

fff' = {{1, 2, {{1, 2}, {3, 4}}}, {2, 
       8, {{0.5, 3}, {1.4, 2}, {3, 13}, {2, 18}, {0.3, 19}}}}

Is it possible with a help of one command such as Select?

Answer 1

Using MapThread:

MapThread[Join, {#[[1 ;; 2]] & /@ 
   fff, #[[All, 3, All]] &@fff /. {x_, y_} /; x > 3 -> Nothing}]

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Using MapAt:

MapAt[If[First@# > 3, Nothing, #] &, fff, {All, 3, All}]

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Using Select:

MapAt[Select[#, First@# <= 3 &] &, fff, {All, 3}]

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Result:

{{1, 2, {1, 2}, {3, 4}}, {2, 8, {0.5, 3}, {1.4, 2}, {3, 13}, {2, 18}, {0.3, 19}}}