noun, noun which may take the genitive case particle 'no'
each point; each item; every detail
Used to refer to individual points or items in a list, argument, or set of details, often in formal or written contexts. Can function as a noun or adjectivally with の.
彼の提案について、廉々検討する必要がある。
We need to examine each point of his proposal carefully.
契約書の廉々に目を通した。
I looked over every detail of the contract.
逐一 means 'one by one' or 'in detail' and is more adverbial, whereas 廉々 is a noun/adjectival form used to refer to the points themselves.
Reduplication of 廉 (かど, 'point' or 'item'), with the iteration mark 々 indicating repetition. The exact historical derivation is uncertain, but the form is used in formal written Japanese.