My fighter has an Aberrant Dragonmark with Green-Flame Blade and Shield. But of course the Shield spell can only be used once a day. If I got a shield spell wrought tattoo, would it use constitution as the spellcasting ability, or would it rely on intelligence like a wizard?

Quote from Dawnrex15 >>

My fighter has an Aberrant Dragonmark with Green-Flame Blade and Shield. But of course the Shield spell can only be used once a day. If I got a shield spell wrought tattoo, would it use constitution as the spellcasting ability, or would it rely on intelligence like a wizard?

 
It's not once per day. It's once per short rest. It can be used multiple times a day.

The use of con as the spellcasting ability only applies to that specific feature/spell. The spellwrought tattoo has no relevance to your stats at all and only uses the figures given in the item description.

Also, Shield spell has no relevance to caster stats. So it doesn't matter what ability you use. 

Cool, thank you ^^

Yer welcome. Happy shielding. :)