The slum dwellers are often seen quarreling with each other which seriously affects the psychology of the children belonged to those families.
I doubt about its use as a post modifier, if any objection please say.
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The use is not correct. Rather than try to force the word "belonged," where it really does not (ahem) belong, I would offer this rewrite:
"...psychology of those families' children."
Again, an analytical struggle over a single word often hints at a structual problem in the sentence rather than with the word itself.