ANSWER:

Removing the ring is not required as the Prophet salla Allahu alaihi wa sallam didn’t do it.

However, it is best to remove both to ensure that that the water reaches underneath it. 

When we are washing our hand we have to remove watch and ring for ablution

Ablution (Wudhu) | September 3, 2018 5:57 am
Previous

Sheikh If Do The Istinjah Put Water In My Mouth Nose And Do Masah And Clean My Arms Then Take My Routine Shower Do My Shampoo And Body Wash Etc Then Wash My Feet. Is My Ghusul Valid? For The Major I.e sexual Impurity? Will It Cover My Wudu Also?
Next

In wudu is it permissible to wipe over normal socks?