Correct spelling for the English word "Pedanticly" is [pɛdˈantɪkli], [pɛdˈantɪkli], [p_ɛ_d_ˈa_n_t_ɪ_k_l_i] (IPA phonetic alphabet).
The word "Pedanticly" is not found in the English language, and therefore it does not have an etymology. It appears to be a misspelling or a combination of two words, "pedantic" and "ly" (which typically functions as a suffix to create adverbs).
However, let's explore the etymology of the word "pedantic" as that seems to be the base word being used here. The term "pedantic" derives from the Latin word "paedagogus", meaning "teacher" or "tutor". It then entered into English in the 17th century from the French word "pédantesque", which meant "like a schoolmaster". Eventually, it transformed into the English adjective "pedantic", referring to a person who overly emphasizes minor details or rules, particularly in a way that displays knowledge or learning.