From a fundamental information theory standpoint, it's can't exist*. For secure voting you need to identify the voter and ensure the voter's ballot is included in the final count. The real problem is that you have to do it in a way that not even the voter can identify their ballot in the list of counted ballots. This is necessary to prevent coerced voting. The only way we can do this is by putting ultimate trust in some part of the system. The primary goal when designing voting system is to make that trusted part as small and as simple as possible. All the things you would need to do to make this is work over the internet is diametrically opposed to both those criteria.

That said, you can absolutely design a very inexpensive, easy to use, secure, computerized voting system if you wanted to. It consists of terminals powered by an Arduino, a basic LCD screen and cheap thermal printer. You can have whatever ballot layout (along with any assistive technologies) and the voter makes their selections electronically. The printer prints a voter-verifiable ballot using the same ballot that is mailed to absentee voters. It's put in the same box as the other votes. A scan and counting machine power by another Arduino counts the ballots and displays the number of votes for each candidate/measure.

Ultimate trust is placed in the code and hardware of the counting machine. While that is fairly complex, it is entirely possible to verify it's operation to a reasonable degree of certainly. If you really wanted to be sure, I could design a counting circuit out of fully viable mechanical relays. Plus you can always just hand recount or run them through machines from a different manufacture.

* Theoretically something called homomorphic encryption might be able to solve this, but we have no working implementation and it massively violates criteria number 2.