Which is better and more rewarding: searching for work outside Madinah in a specific engineering field to benefit Islam and Muslims, or continuing to work in Madinah in an undesirable field, or waiting for a desirable job opportunity in the same city?

Residing in Madinah is commendable, and Imam Ahmad preferred it over staying in Makkah for those who can endure its challenges, due to the Ahadith that explain the virtue of patiently bearing its hardships, and that the Prophet, peace and blessings be upon him, will intercede for whoever dies there.

However, if departing from Madinah is for a preponderant benefit that accrues to Muslims, such as spreading knowledge or engaging in Jihad, then there is no harm in it; rather, it might be more virtuous, as the Companions, may Allah be pleased with them, did. Therefore, staying in Madinah is better for you, unless there is a preponderant benefit in leaving it, and your departure brings a public good to Muslims.