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The phrase "a much smaller amount" is correct and usable in written English.
It can be used when comparing quantities, indicating that one quantity is significantly less than another.
Example: "The new budget allocates a much smaller amount for marketing than last year."
Alternatives: "a significantly lesser amount" or "a considerably reduced amount".
Exact(60)
In practice, a much smaller amount is likely to be recoverable.
The new device reads a much smaller amount of DNA than larger, more expensive machines.
Aquaculture generates about $75m in annual revenues for Pentair, aquaponics a much smaller amount.
Others, however, will walk away empty-handed or with a much smaller amount than they wanted".
A much smaller amount of funding for the dam project, $1.7bn, had been agreed during earlier legislation in the House.
If you have a much smaller amount in savings, the benefits of the personal savings allowance are negligible.
A country with even moderate technical expertise could achieve the same yield with a much smaller amount.
A court later awarded her a much smaller amount after it emerged that the child was not Mr. Kerkorian's.
It found poverty declining among Latinos, though by a much smaller amount than it declined among blacks.
She said a much smaller amount of chlorinated sewage from the original leak would be reaching the Hudson at Yonkers.
Due to the practical issues of manually transcribing the data, there is a much smaller amount of word-labeled training data than ICSI scientists would prefer to have.
More suggestions(14)
a very smaller amount
a much smaller quantity
a much less amount
a much smaller volume
a substantially smaller amount
a further smaller amount
a considerably smaller amount
a much smaller sum
a significantly smaller amount
a considerable smaller amount
a much higher amount
a much smaller fraction
a much smaller proportion
a much smaller value
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com