In its each side with tower clock dwindled its ringing tone

没有语法错误 但不是一个完整的句子 可以理解成一个独立主格结构作为某个主句的伴随状语
In its each side 和 in such a ten-mile street都是地点状语
你只要看主干
with tower clock dwindled its ringing tone 就行了
典型的with +独立主格的句式风格
ps:重新看了一下 觉得还是有错误的 dwindled应该用进行时dwindling

On each side of the tower is a clock that strikes every hour on the hour dwindling its ringing tone over such a ten-mile-long street.

错误有点多，试着帮你改动一下：
on each side, there is a tower clock with ringing tone that dwindles along sunch ten-mile street.
每一边/面都有钟，其报时声音沿着十里长街逐渐减弱。
不知道是否符合你要表达的意思，供参考

In each side of it is a tower clock .....