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The phrase "a relatively small portion" is correct and usable in written English.
It can be used when discussing a part of a whole that is not large in comparison to the entire entity.
Example: "In the survey, a relatively small portion of respondents indicated that they were dissatisfied with the service."
Alternatives: "a minor segment" or "a limited fraction".
Exact(60)
Its asset-management fees plummeted 77 percent, to $5.6 million, from the period a year earlier, though the division accounts for a relatively small portion of the firm's total revenue.
These Parsi (Persians) have preserved only a relatively small portion of their sacred writings.
Participation in the political process is limited to a relatively small portion of the population.
SRI constitutes a relatively small portion of overall investment activity but is gaining popularity.
Impact investing, still a relatively small portion of philanthropy, could also face growing pains.
She has added 22 patches in a relatively small portion of the tail.
What's surprising is that it is a relatively small portion of our costs.
Ms. Byrd and other homeowners in her situation make up a relatively small portion of the national housing market.
Sony also got substantial contributions from its video game division, which accounts for a relatively small portion of overall sales.
Instead, they've both buckled under a business — mortgages — that accounted for a relatively small portion of profits.
A relatively small portion of the company is publicly traded, and that portion will be soon diluted further.
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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