There was a clone by Timex, the T/S 1500, which was a ZX81 (with 16 kB RAM!) in a Spectrum-like case with rubber/chicklet keys: https://en.wikipedia.org/wiki/Timex_Sinclair

You can build your own ZX81 replica, there are several projects available and all components are still available since the replicas replace the Sinclair ULA with a bunch of regular 74-series TTL ICs. We used the ZX81plus38 for a soldering course with our students, this works very well:

https://github.com/mahjongg2/ZX81plus38

There's also a Sinclair Spectrum clone, the Harlequin, which is also quite simple to build.