The interjection nope is first found in print in 1888, although it was likely common in speech well before that. Essentially, when you say “no” quickly and crisply, closing your mouth causes the final vowel to sound like it ends with a /p/. This is because a final /p/ sound is usually made by closing both lips. This phenomenon has the charming name “excrescent p”. Excrescence is the general term for a sound change where a consonant gets added to a word, like the /p/ sound often found in the middle of something or hamster when spoken aloud.

The parallel yep, likely based on yeah, is similarly first attested in 1882. Here’s a 1946 paper where a linguist discusses the phenomenon, including an example usage of welp, based on well, long before its first print usage in the wild in 1987. Welp saw a dramatic rise in usage in the late 2000s and early 2010s, as captured in this 2012 Slate explainer about the word. The regional ope is likely a similar alteration of oh.

Icon with the word "Nope!" in white text over a purple diamond from the video game Balatro Icon with the word “Nope!” in white text over a purple diamond from the video game Balatro