[OP] This was to be done using an extremely potent poison that was supposed to be sprayed on him topically and kill him within a few days without a trace (a "quiet" murder).
Poisons leave a trace. In the case of fentanyl derivatives, which are dangerous in very small doses, it is technically challenging to find the trace, though. The path of entry is described differently by different sources. Some speak of "injection" into the ear while others say the intent was to spray on the back of the neck, but Mashal supposedly turned his head to the side, and the spray went into one ear.
[OP] It was probably an internal formulation of the Mossad,
I did not find any evidence, or even other claims, for this.
[OP ...] but I was wondering if the formula was ever publicly released or if anyone knows how Fentanyl's structure was modified in order to make it so deadly upon contact.
In general, fentanyl and its derivatives are contact poisons (see airhuff's comment to the OP's question). As of 2022, I don't think Mossad disclosed which substance was involved. However, this peer-reviewed medical paper comments on reports claiming the use of the fentanyl derivative carfentanyl by Russian safety forces in an anti-terrorist case:
Carfentanyl has also been reported to have applications in anti-terrorist interventions as incapacitating agent, used by Russian safety forces in the hostage rescue operation in October, 2002, in the Dubrovka theatre, Moscow. Carfentanyl and remifentanyl were found on a shirt sample and carfentanyl metabolite norcarfentanyl was found in a urine sample. It is possible that an aerosol containing a mixture of carfentanyl and remifentanyl was used.
If the poison was indeed a fentanyl derivative (targeting the opioid receptors), a possible antidote would have been naloxone, approved in the U.S. since 1971 to treat opioid overdoses. It competes with opioids, so the stronger the opioid binds, the higher the necessary does of naloxone (for the example carfentanyl, 100 mg of naloxone are administered to treat a 1 mg exposure with carfentanyl).
[OP] I've been trying to figure out how fentanyl could have been modified, but have no clue either.
Fentanyl itself is a synthetic product. The derivatives, of which many are known and characterized, are not always obtained by using fentanyl as a starting material. Sometimes, they are made using a different series of synthetic steps. So derivative (or modification) often refers to similarity in structure, not necessarily making a claim about the path of synthesis.