The first portable digital camera was likely the Fuji DS-1P from 1988, that's the predecessor of modern DSLRs. But we'll turn your attention to the Game Boy Camera instead - a 1998 accessory for the Game Boy that was credited as the "world's smallest digital camera" by Guinness World Records. It plugged into the cartridge slot and took photos with 256 x 224px resolution and 4 black levels (it couldn't capture color). The camera came with a built-in image editor (presaging Snapchat's filters) and animation (HTC Zoe, the early days). You could even buy a printer, similar to the ZINK...
Source: http://www.gsmarena.com/counterclockwise_sony_ericsson_t68i_nokia_7650_and_the_rise_of_the_camera_phone-news-24435.php