The correct spelling of the phrase "sticking there" is /stɪkɪŋ ðɛr/. The word "sticking" is spelled with a "-ck-" as opposed to a "-cc-" because the root word "stick" ends in a consonant sound. The word "there" is spelled with an "-e" at the end to represent the schwa sound /ə/ and to differentiate it from the homophone "their." Therefore, when written phonetically in IPA, "sticking there" should be spelled as /stɪkɪŋ ðɛr/.
The phrase "sticking there" is not a stand-alone phrase with a specific etymology. However, the words "sticking" and "there" each have their own etymologies.
The word "sticking" comes from the Old English word "stician", meaning "to pierce" or "to stab". It can also refer to something being fixed or attached to something else. The etymology of "sticking" relates to the Middle Dutch word "steken" and the Old Saxon word "stekan".
On the other hand, "there" stems from the Old English word "þǣr" or "þēr", which ultimately derives from the Proto-Germanic word "*þaer". The meaning of "there" is primarily used to indicate a place or location, often indicating a location away from the speaker or the person being addressed.