"Ud's pity", in Shakespeare, is glossed as: "God's pity."

What is the origin of "Ud's" ?

For what it's woprth (maybe not much), it's often written with a leading apostrophe, ie, 'Ud's pity, suggesting an abbreviation for God, possibly in another language

Not a far cry from "'Swounds" or "Zounds" meaning "Gods' wounds"

Or Odd's bodkins.