The unfortunate thing about Whites is that there is no straightforward answer to "what will White crossed with X color look like?"
Think of White as a coat of paint. Whites are not genetically white, they are another color with a "coat" of white "paint" over the top. They may be Partridge, they may be Blue, they may be Cuckoo. There is simply no way to know just by looking, because the white gene (either I/I or c/c) acts like a coat of paint over it all, switching off all pigment in the feathers.
The typical White in Silkies is recessive (c/c). Very rarely you will find a dominant white (I/I) Silkie, but it's not common. I don't know how much you know about genetics but recessive means you need two copies of the gene for it to show. So if a bird is recessive white, you will only get white offspring by A. Crossing a white with a white, B. Crossing a white with a white carrier (C/c), or C. Crossing two white carriers together. So unless your Partridge bird is carrying recessive white for some reason, the offspring will look like Partridge x whatever color the white is hiding. For example, if the white was genetically Blue, the E and Bl genes would take over and you'd get 50% black and 50% blue offspring, who would also carry the white gene (and could produce white offspring if bred back to a white or white carrier).