Which is the correct Trayakshar Mrityunjaya Mantra- Om Haum Joom Sah OR Om Joom Sah
The correct Tryakshara Mrityunjaya Mantra is Om jum sah, the 2nd one you gave.
Sarva Devadevi Mantra Koshah (Mantras collected from Tantras for all deities-complied by Upendranath Mukhopadhyaya) gives the following Mantra:
Atha mrityunjaya mantrah:
TAram sthirA sakarnendu bhriguhusarga samnvitah |
TryakshAratmA nigadito mrityunjaytmakah ||
Om jum sah || (1)
The Mantra first is given in a code (as is usual in Tantras).
Some hints to decode it are as follows:
TAram - TAraka Mantra or Om.
Sthira - referring to the letter Ja.
Bhrighu - referring to the letter Sa.
Sarga - Visarga (:)
The 1st Mantra that you gave is not given in the book under Shiva Mantras. So, it may or may not be a valid Mantra. But, whatever might be the case, it is not a 3-lettered Mantra. It is 4-lettered as you can see.
The text also gives another form of the Mrityunjaya Mantra which is not 3 but 12-lettered:
Mrityunjayam samucchArya pAlaya dvitayam vadet |
Mrityunjayam samucchArya punareva vilomatah ||
DwAdashAksharam mantrohayam mrityunjayAbhidhoparah ||
Om jum sah pAlaya pAlaya sah jum Om || (2)