Purple color at the cuticle of nails can be caused by a number of reasons, and it would always help to seek advice from a dermatologist for an in-depth assessment. Purple nails close to the cuticle could be a result of trauma or injury on nail bed, like banging fingers and its related areas. Circulatory problems, pre-existing medical conditions or certain drugs might be responsible for discolored nails. It may also be associated with inadequate oxygenation or blood supply to the nail matrix. Dermatologist will be able to provide an accurate diagnosis and suggest suitable treatment depending on the circumstances.

Purple or bluish discoloration may be because of less oxygen or irritant or allergic contact Dermatitis... You need to consult dermatologist for detailed examination also