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I created a role in Configuration. Now, i want to give editing rights to only one of the attribute and not to other attribute of that entity for one particular role.

Yes it is possible to give editing rights to one of the attribute of an entity for a particular role

Go  to the model privileges Grant click on the role 

Under the entity privileges click on the entity where you want to give the editing rights to a certain attribute

Now under grant section select read/write for the attribute also enable allow creation and allow checkout,

note : you will not be able to edit if you do not check on allow checkout