wir gedenken seiner in Ehrfurcht.
I have only understanding about genitive personal pronouns is that it is used with genitive verb like in above given example though I would like to know that Is there any other way to use genitive personal pronouns or Is it only used with genitive verb?
German case inflection is governed mostly by verbs and prepositions. You've seen how genitive verbs (very rare) work.
Genitive prepositions can in principle govern the same forms. For instance,
Don't bother on my account
could translate to
Mach Dir wegen meiner keine Umstände
but in practice, the incorporated form meinetwegen/seinetwegen etc. is used instead. Some other genitive prepositions are semantically unlikely to take personal pronouns, e.g. "gemäss", "innerhalb", or "während". Perhaps the most commonly used is "statt", which is semantically rather generic, so you do occasionally see the phrase "statt meiner"; but even this is more often said as "an meiner Stelle".
Finally, cases can occur motivated by an entire construction rather than a governing word. A recent example here showed how a dative can express beneficiary semantics without a verb: "Dem deutschen Volke" (to the German people). There is such a constructino with the gentive, which expresses possession:
Die Höhle des Löwen = the lion's den
In theory this could motivate constructions such as *"Das Auto meiner", but again, this is never done, since we have possessive pronouns for that task: "mein Auto".
Overall, then, genitive pronouns are much more likely to be worked around than used. It's probably safe to say that they are threatened by total extinction.
Genitive forms of personal pronouns are used with certain adjectives:
als wir seiner ansichtig wurden
Er ist ihrer überdrüssig geworden.
Dieser Kerl muß sich seiner sehr sicher sein.
Das Ich ist nur insofern, inwiefern es sich seiner bewußt ist.
Sie schmissen ihn und seine Leute, als sie ihrer gewahr wurden, sofort hinaus.
