Sorry, you can not get twins on a Tamagotchi Connection / Connexion V1, V2, V3, nor V4.
It has been rumored for almost 10 years now, that it's possible to get two eggs at the same time on one Tamagotchi, and raise them together. Apparently, through ROM Testing on some of the original Tamagotchis (from 10 years ago), it was possible to make two eggs appear on the screen. However, these did not behave as independent characters.
There are a few photos of twins that keep circulating. These are either of the original Tamagotchis that have been ROM Tested, or they are faked photos.
The misconceptions:
The only times you can have two Tamagotchi characters on your Tamagotchi Connection/Connexion at the same time are (1) in the case of a parent and child, and (2) temporarily such as when connecting, or playing a game.
Some people say that a Connection/Connexion can get twins. However, further investigation reveals that what they are talking about are the two babies that are produced when two Tamagotchis mate. The problem with this is that within a few seconds of their birth, one of the babies flies off to live with the other parent.
There are passwords from the Nintendo DS game "Tamagotchi Corner Shop" and "Corner Shop 2", which when entered into the Connection/Connexion V3 and V4 will give you what some people call a twin. In reality, the password gives you an item labeled "!!", which can be used by an Tamagotchi character to summon a clone of itself. Your Tamagotchi character and its clone will then dance together for a few seconds before the clone disappears. (Note: on the V3, only adult characters can use the "!!" item.)
The reality:
If twins really did exist, proof of their existence would not be so elusive. If I had twins, I'd be taking photos of them doing all kinds of different activities, eating, playing, sleeping, even using the toilet, and posting these all over the place. Wouldn't you? So if someone out there has had twins, why can't we find these photos? Answer: twins on a Connection/Connexion are a myth.
