Child Class:

public class Child{

    public String Name;
    
    public Child(String name) {
        this.Name = name;
    }
}

Parent Class:

public class Parent{

    public Child[] ChildRecords;
    public String Name;
    
    public Parent(String Name) {
        this.Name = name;
        ChildRecords = new Child[0];
    }
}

Pass parameters to above class using below code:

//Select Account Id from Account Object
String accountId = '0012800001A4UgG';

//Select Account & Contact Records
Account acc = [SELECT Id, Name, (SELECT Id, Name FROM Contacts) FROM Account WHERE Id =: accountId];

//Create a parent record
Parent par = new Parent(acc.Name);

//Loop on Contacts
for(Contact con: acc.Contacts) {
    par.childRecords.add(new Child(con.Name));
}

//Get the Json data
String jsonData = JSON.serialize(par);
System.debug('JsonData-' + jsonData);

Here is the debug log snapshot of Json data:

Note: This is the sample class. You can modify it as per your requirement.