Should I use the word 'jete' for 'drop' when I say "drop me off at the school' for example?

No.

Drop off - lage, depoze

Drop me off here. - Lage m la.  or Depoze m la.

Drop me off at the school. - lage m nan lekòl la.

Drop her off at the school. - Lage l nan lekòl la

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