Does the word '县子‘ exist？
子 in words like 筷子, 裤子 is a padding to make single character words fit into modern Chinese which favours double character words. Most Chinese people picked them up as they build vocabulary and aren't taught any rule on formulating these.
However, if you want a rough rule, then 子 is like the English suffix '-let' which only fits on nouns that can be seen as small.
In Chinese thinking, only 村/village is small enough to be called 村子.
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However, to avoid the awkwardness of using the single-character geographical words 省/城/县/乡/镇/etc, other suffixes like &quot;里&quot; are used instead.
For example, 看这个病得去省里/城里/县里/乡里/镇里 (This disease can only be treated in the [nearest] provincial [capital]/city/county/township/town).
&quot;里&quot; obviously means inside, which is more fitting for larger geographical areas.