The phrase "a modicum of his" is correct and usable in written English.
It can be used to refer to a small or limited amount of something that belongs to him, often in a context where you want to emphasize the scarcity or insufficiency of that thing.
Example: "Despite his talent, he only showed a modicum of his potential during the competition."
Alternatives: "a small amount of his" or "a little of his".
André is a strong man, I hope he can find a modicum of his definition".
It was the irony of this man's success at hawking happiness, while struggling to find a modicum of his own that Weiner wanted to communicate.
Had he used a modicum of his considerable power to overrule Curley and direct him to call the police immediately, he could have saved countless other victims, the shame and damage to Penn State, and the tragedy of his own shattered end as a president.
Though his myriad gifts as a novelist lend the resulting story more than a modicum of suspense, his two central characters remain paper-and-paste constructions, assembled out of a bunch of outrageous anecdotes and devoid of any sort of coherent inner life.
A modicum of stability during his childhood was provided by his aia (governess), Dona Maria Genoveva do Rêgo e Matos, whom he loved as a mother, and by his aio (supervisor) friar António de Arrábida, who became his mentor.
If Mr Saleh cannot soon bring a modicum of prosperity to his people, the spirit of revolt may seep into his own back yard.
But with the help of Ravichandran Ashwin (20), Dhoni managed a gritty unbeaten 57 - his maiden fifty on Australian soil - to hand a modicum of respectability to his side's total before he ran out of partners.
Dressed in a three-piece business suit, Mr. Gantner preserved a modicum of dignity despite his humiliating performance in the song contest.
But the Oracle of Delphi continued, burying a modicum of hope in his inscrutable message: "Though all else shall be taken, Zeus, the all seeing, grants that the wooden wall only shall not fail".
But it seems he could have just as easily come out and acted contrite, taken some responsibility for BP's actions, and conveyed at least a modicum of knowledge about his company's activities.
However, he asks, "Is it an Arab name from the Koran or purely a Somali name?" James intends to impress Ahmed; he wants the young man to know that he has a modicum of knowledge about his traditions.
