"Wow. That's really what you're going with? You know, just do the water drinking bit." — Li'l Jeet[source]
"Aren't you the dummy from the comedy show?" To Baljeet "She's talking to you..." — Candace Flynn, Li'l Jeet[source]
Baljeet's Puppet (also called Li'l Jeet by Baljeet) first appeared when Phineas and Ferb tried to cheer up Candace with a Ha-Ha-Hut where the puppet was controlled by Baljeet. The Puppet was also used to send an invitation for the Mix and Mingle Machine to Candace ("Cheer Up Candace").
During Candace's (actually Perry's) dream, a similar puppet appeared. The puppet was initially thought to be Baljeet, who was controlling puppets of Linda and Lawrence until "Baljeet" was revealed to be a puppet himself that was controlled by the Talking Zebra ("Phineas and Ferb Get Busted!").
Li'l Jeet is similar to Mini Squid from the show Spongebob Squarepants in the fact that he is a puppet made in the image of a character on the show and they are both named according to their size with a nickname or shortened version of the names of the characters they're small copies of.