Persian az is from OP hača (with common OP č > MP/NP z) cognate with Sanskrit sáčā (Mayrhofer seems to relate it PIE *sekʷ- "to follow", cognate of "sequence"). German aus and English out are from PGrm *ūt itself from PIE *ud which became *uz in Iranian. It survived in Persian as part of a few verbs like zodūdan (PIr. *uz+dauH).
y > j is a common sound change in OP>NP. Nyberg assumes that جدا is from yuvat- (MP "separately") > *yut (e.g., Parth. ywd). He considers it from *vi-vāta. By the way, joz (جز) is apparently from the same root (< jud+az). They are cognate with forūd (*fra-vata).