What is the name of the recurring viral infection that produces fever blisters or cold sores?

The name of the recurring viral infection that produces fever blisters or cold sores is Herpes simplex. This virus is known for causing sores on the lips and around the mouth, which are commonly referred to as cold sores or fever blisters. The Herpes simplex virus is highly contagious and can be triggered by various factors such as stress, illness, or exposure to sunlight.

Shingles, which is often mistaken for Herpes simplex, is caused by the varicella-zoster virus, the same virus that causes chickenpox. While it can produce painful rashes and blisters, it does not typically result in the recurrent cold sores associated with Herpes simplex.

Psoriasis is an autoimmune condition characterized by the rapid buildup of skin cells, leading to scaling on the skin's surface. It does not relate to viral infections and does not cause cold sores.

Verruca refers to warts caused by the human papillomavirus (HPV). These are different from cold sores and arise from a different type of viral infection.

Thus, Herpes simplex is the correct choice as it directly correlates to the production of fever blisters or cold sores, differentiating it from other conditions and viruses.