Can I use yellow zinc coated construction screws on shower brass fitting?
Yellow construction screws are commonly zinc chromate plating over a steel screw. They are softer than drywall screws and work better in structural applications. They are stronger and take stress better than hardened and brittle drywall screws.
They are not suitable for wet applications, such as decks, and if the zinc chromate plating gets chipped or worn off, the fastener will rust. They are not recommended for applications where they contact dissimilar metals, where corrosion is likely to occur readily.
The result will not be what you desire.
I suggest that you procure brass screws, and use those. They will work in the shower setting much better, and you will not have incompatible metals creating a corrosion issue.