The Twist name has been used by Giant on several models, but I suspect yours may be
this one, either step-through or crossbar.
If so, the only one that suits for fitting into the original position is that £300 NiMh one from Giant. There aren't any makers of compatible batteries for various e-bikes, the market is too small as yet and there are rights issues on the cases and mountings. Some companies who have tried recelling these batteries have had problems and abandoned it.
Much the same applies for the later Twist models with one or two pannier type batteries, either lithium or NiMh, the only correct fitting replacements are the Giant ones.
The only realistic alternatives for the Twist models is to buy another make and mount it on the carrier, adapting the wiring connections as necessary, but there won't be much saving if any.