a mix of the words mayhaps and happenstance which in turn are a mix of the words maybe-perhaps and happen-chance
together it means : perhaps, maybe by chance /he/she/it just happened to be that...
mayhappenstance is used to save time speaking except when the other person asks for an explanation hence more wasted time trying to explain and thus being ironic
maybe and perhaps equals mayhaps, and the end of perhaps, "haps", is the beginning of happenstance: ergo, mayhappenstance. It's supposed to be used in a surrealist, ironic, or joking manner to mean maybe. However, use it with caution: you might need to explain yourself afterwards.