I've been reading Yotsuba and in this part, when talking about these two sisters, Yotsuba asks: “追いかけてくる方か？強い方か？きれいじゃない方か？”. I'm assuming this is a way to say "The (qualifier) one", but I'm not finding anything directly explaining this on the internet lol
You are correct in reading 方 as ほう. I am going only on what you've quoted in text in the question, but 方 here almost certainly definitely means "type" or "one," something chosen between options. The translation would be:
"The one who comes running to you? The strong one? or... do you mean the non-pretty one...?" (on that last part I am here reading into the possible emotions but believe this is probably what is going on, not knowing the source of what you are referencing)
ほう's literal meaning is "direction", and it is used to turn things into options to choose from. For example, you can say to a child who doesn't want to get the vaccine shot:
When used to refer to a person, it gets confusing because 方(かた) is also used to refer to a person (without making them into options). For example, you can say あの方は誰 and that usage doesn't imply they are an option. To my knowledge, 方(かた) as a way to refer to a person has also evolved from the original meaning of "direction".
You cannot use ほう in the same way as かた, i.e. a generic way to refer to a person. It can only be used when you are turning people into options.
Importantly, if you say 方(かた) to refer to a person, it's polite. Whereas if you say ほう then it's almost disrespectful (if you are e.g. 先輩 in a sports club situation then it might be acceptable). This is also why I can confidently say in this instance it must read ほう because the context is not a polite context.
If it's 外国の方ですか、それとも日本の方ですか then I would read it as かた as the polite context implies it's used as かた