The correct spelling of the phrase "paying way" is /ˈpeɪɪŋ ˌweɪ/. The first word, "paying", is spelled with a "y" because it is derived from the verb "pay". The second word, "way", is spelled with a "w" because it is not pronounced as "v" in English. The combination of "a" and "y" in "paying" creates the diphthong /eɪ/, while the combination of "w" and "a" in "way" creates the vowel sound /eɪ/ as well. This is why the spelling of "paying way" is as it is.
There is no specific word "paying way" in English. However, if you are referring to the phrase "making your own way", it means to achieve success or progress through individual efforts, without relying on help or support from others. The etymology of this phrase is as follows:
"Making" comes from the Old English word "macian", meaning "to make" or "create".
"Your" is a possessive pronoun indicating ownership or association with the person spoken to.
"Own" comes from the Old English word "āgen", meaning "one's own" or "belonging to oneself".
"Way" comes from the Old English word "weg", which ultimately derives from the Proto-Germanic word "*wegaz", meaning "path" or "road".
So, the etymology of "making your own way" indicates the concept of independently creating and following your own path towards success or achievement.