jq: Cannot index array with string

It should be:

jq '.[].aux[].def' file.json

.[] iterates over the outer array, .aux[] then iterates over the the aux array of every node and .def prints their .def property.

This will output:

"I want this"

If you want to get rid of the double quotes pass -r (--raw) to jq:

jq -r '.[].aux[].def' file.json

Output:

I want this