I found two noun words such as Specificity and Specification. When can we use Specificity over specification.
The short answer is that specificity refers to a quality and specification refers to a description of a subject. You could give specification of specificities ;) They are both nouns, but they operate in different ways.
Specificity is word of denoting a resolute characteristic. The components of microprocessors reflect the tremendous specificity involved in their development and a decent baker or chocolatier works with similar specificity. Whether used with another noun or verb, specificity is a quality, trait, or characteristic of the subject.
Specifications describe something. Unlike specificity, specifications are removed from the subject itself. By that I mean that specification is not the object itself but how the object is perceived (or designed) by an observer. Amazon lists an item's specifications to cover important details of an object and mechanized manufacturing excels at making objects that conform to specifications. Specification describes (or prescribes) the qualities of a subject, typically an object.
Keep in mind that specificity has special significance in chemistry and biology not covered above. Here's an example of that usage.
Specification generally refers to some sort of categorization or set of instructions: "The specifications for building the house were delivered by the architect." Specificity refers to the clarity of something: "Without knowing what sort of wood the architect wished them to use, the contractors could not shop with any specificity."
Specification: an act of describing or identifying something precisely or of stating a precise requirement.
Specificity: the quality of being specific rather than general