Short answer
For a small cat, a spoonful of jam is low risk but not ideal. The main concern is the sugar content, which can cause an upset stomach. Watch for mild signs like vomiting or diarrhea over the next day. If those appear, or if you ever suspect xylitol in a sugar-free jam, contact your veterinarian.
Jam / jelly — Food safety facts
Feed with care · Cats · full breakdown on the linked food page
Sugar, and sugar-free versions may use xylitol. Grape jam adds grape toxicity.
The full verdict, portion guidance and serving notes are collected on the Jam / jelly food facts page.