Hi Yowaraj,
I don't think it's easily possible to do through a standard page builder widget property. It might be possible to do something JS based if you can figure out how to trigger that script within the property modal (e.g. replacing a required asterisk placeholder in the label with a styled star).
What you could do instead as an alternative, is just add an unstyled asterisk as part of the property's label:
[EditingComponent(DropDownComponent.IDENTIFIER, Label = "Venue *", Order = 1)]
public string Page { get; set; }
Or you could add explanation text to this property so at least there's an indication that the field is required:
[EditingComponent(DropDownComponent.IDENTIFIER, Label = "Venue", Order = 1, ExplanationText = "Field is required *")]
public string Page { get; set; }