Having grown up in central Indiana and also having a scouting background and working with kids myself, this is the version that I've always seen played, which has three verses, though the second verse tends to get omitted fairly often, and sometimes we only use the first verse...

Down by the banks of the hanky panky
Where the bullfrogs jump from bank to banky
With an eeps! Ipes! Opes! Oops!
And an oop flop a dilly and an oop flop flop

Pepsi cola came to town
Coco cola shot him down
Dr pepper fixed him up
And now we all drink 7up

Pepsi cola ginger ale
Ginger ale ginger ale ginger ale ginger ale
Pepsi cola ginger ale
7up 7up 7up you're out

The game is played in a circle with everyone sitting with their palms up, left hand under and right hand over the person's next to them. A leader is chosen to start the hand slap, which is passed around the circle. When the song ends, the person it stops on is out, and the person to their left becomes the new leader. When it gets down to two people, they join hands and move their arms in a saw-like motion until the song ends. Whoever has their arm extended wins!

The other ways I've seen online are neat, too, and though I still have a soft spot for the version I learned as a kid, I'm guessing the original third line of the rhyme dealt with a frog hopping and then the original fourth line (which I'm guessing was probably the last line) dealt with a lillypad and a kerplop!

Since children's songs like this are passed down by word of mouth, and children mishear and misspeak lyrics all the time, I don't think the original version is out there anymore, though that one post about the Pasquotanky might be pretty close, since hanky panky is easier to say and remember. However, even that could have been changed to fit the location of the children singing it at the time, so it's probable that the only original words to the song were "the bull frogs jumped from bank to banky". Whether the original was "down by the banks of the" or "down by the river of" is still up for debate. Other words could fit there and make sense, too, such as shore or bed instead of banks or river, so even those two could be changed versions of the original, though I think it's more likely that it was river instead of banks first, since banks appear twice more in the second line, and it would be easier to remember for a child if all the things pertaining to water were the same word. Chances are that if it was indeed originally "down by the river of", there was probably no "the" after the word "of" because rhythmically, the word "the" wouldn't fit as well before the name of the river.

Despite all this, do I intend to sing it any differently from what I always have? Nope! While most of the other ways are really neat, I've got a bit of sentimentality for the one I grew up with, so that's the one I'm sticking to.

I hope everyone has an awesome day!
Over and out,
Sarah