I applied for a patent for utility model, and what others did was only part of it. Everything else is the same. Is this an infringement?

Whether it is infringement depends on how you write your claim. If the difference in this part is the necessary technical feature in your claim, then the other party will not infringe.

For example, your patent is a chair, which is characterized by including legs, a supporting surface and a backrest.

The stools produced by the other party, including legs and supporting surfaces, lack a backrest, so the other party does not infringe.