Nope. You have to specify all of the fields you want returned OR you get them all. To make life easier, though, you can copy and paste the field names you want returned in your query. To get the list of available fields to copy, you can view the properties of the layer from your service in the REST API and just delete the unwanted fields and text. From your service, click the Layer Name / ID you wish to "filter" and then scroll down toward the bottom to get the Fields section. Copy all of it to something like Notepad, then delete the extra stuff and bullets you don't want. You can then insert the trimmed-down, comma-separated list of fields into your REST query.