The phrase "a modest part" is correct and usable in written English.
It can be used to describe a small or humble portion of something, often in a context where the size or significance is being downplayed.
Example: "She played a modest part in the project, contributing only a few ideas during the brainstorming sessions."
Alternatives: "a small role" or "a minor contribution".
That's good, but it's only a modest part of the story.
That's a modest part of our corporate philanthropy, but it's increasingly something that our employees do.
The remarks of bin Laden and Zawahiri play only a modest part in Naji's work.
"We ask our employees to share a modest part of that".
Even further afield for Google is Motorola's involvement in making television set-top boxes, a modest part of its business.
True, Bill Gates and Steve Case, chief executives of Microsoft and America Online AOLL) respectively, played a modest part.
I played a very modest part in a fairly big White House entourage for a while.
As something of an expert on constitutions — he is the United Kingdom's representative on the Venice Commission, a body that was created by the Council of Europe in 1990 to give constitutional advice to nations emerging from the dissolution of the Soviet empire — he played what he has referred to as "a very modest part" in the process that produced a constitution for the new South Africa.
"Their money is just a quite modest part of what they do for you because these are smart, successful people who care about the institution.
Expenditures on diplomacy and foreign aid make up a very modest part of the over-all budget, and virtually all national-security experts agree that they promote America's "soft power": its ability to advance its interests without resorting to military force.
Smoking before and during pregnancy was considerably more common in Roma women but it statistically explained a relatively modest part of the excess of poor birth outcomes of Roma mothers.
