You gotta explain your problem more specifically

use screenshots

Can't really understand what's your problem TBH

this is my prisma schema

it does not work

What do these look like?
import { Category, Color, Image, Product, Size, Subcategory } from "@prisma/client"
What kind of errors do you get, and where?

i am not getting any error it just dont adds the data , nothing happens practically

So what you're saying is you are using a multiselect component but when you submit you get nothing as output?

i get this , but i am not sure what i am suposed to do next

It looks like everything is working, what happens if you log the selected and sizeList and change the selected values?
Are they showing the correct selections?
If so, you just need to store the resulting arrays as json in your DB.

yes they are showing the correct, but i cant register the array of data

Are you passing initialData every time? Because in your onSubmit you have

if (initialData) {
        await axios.patch(`/api/${params.storeId}/products/${params.productId}`, {...data, sizes: sizeList, colors: selected});
      } else {
        await axios.post(`/api/${params.storeId}/products`, data);
      }

But your formSchema doesn't include sizes or colors so if no initialData is passed then it will use the POST action without sending the sizes and colors

If you have initialData, then try logging the received data in your API route and see if you have sizes and colors.
If they are there, then the issue must be when you're trying to mutate your DB, likely because of schema/model and accepted data type for the columns being different.

yes i made some modifications but this one is hard