Deep Cheep

Deep Cheeps are a special variety of Cheep Cheeps that are first found in Super Mario Bros. 3 They act and appear to be regular Cheep Cheeps, except for the fact that these creatures are green and will actively chase Mario or Luigi in underwater levels depending on the direction they swim. Deep Cheeps will only give up pursuing Mario or Luigi if they swim behind and past them. Deep Cheeps behave in a similar way to Rip Van Fish from Super Mario World.

New Super Mario Bros.
In New Super Mario Bros., Deep Cheeps and their larger variant, the Big Deep Cheep, only appear in World 6-5. They chase Mario or Luigi until they swim away.

New Super Mario Bros. Wii
In New Super Mario Bros. Wii, they are slightly more common. One appears in World 1-4 along with a Big Deep Cheep. If Mario and co. keep staying in the area, another pair appears. They also appear in the second part of World 8-4. In this game, their mouths have become pink, like a Cheep Cheep, rather than the red-orange color they previously had. Their fin and tail have also become yellow, as opposed to white. There is a more relentless enemy similar to Deep Cheep known as Spiny Cheep Cheep.

New Super Mario Bros. 2
Deep Cheeps reappear in New Super Mario Bros. 2, where nothing has changed about their behavior and appearance since New Super Mario Bros. Wii. Deep Cheeps first appear in.

New Super Luigi U
Though Deep Cheeps did not appear in New Super Mario Bros. U (despite them receiving official artwork for that game), they reappear in its expansion pack game New Super Luigi U. Their only appearance is in Cheep Chomp Chase.

Mario Party 9
In Mario Party 9, a Deep Cheep can be seen swimming around Blooper Beach. It jumps out of the water at various intervals and may even jump over the player's vehicle. It has no effect on the gameplay. This may just be a green Cheep Cheep as there are many of these in the Mario series.

Super Mario Maker
Deep Cheeps reappear in Super Mario Maker. They replace green Cheep Cheeps in the New Super Mario Bros. U style, except that they no longer chase the player due to the green Cheep Cheeps and the Blurps not being able to chase Mario. Furthermore, the voice heard when placing elements onto the course will still call them Cheep Cheeps.

Trivia

 * Deep Cheeps have the same color scheme as a Mr. Kipper out of water in Super Mario RPG: Legend of the Seven Stars.
 * A green variety of Flopsy Fish appears in Yoshi's New Island, possibly as an allusion to Deep Cheep.
 * The gray Cheep Cheeps in the original Super Mario Bros. were recolored green in Super Mario Bros. 3 and Super Mario All-Stars, bearing some resemblance to Deep Cheeps.