OWL subclassing vs new properties for existing classes

There is no need to create a new class. That's kind of the whole reason the Semantic Web uses URIs as identifiers - it allows terms defined in one ontology to be directly reused in another.

While you don't have to create a new class, you still CAN do so by giving some semantic constraints. So, going with your example of my:Person being a subclass of foaf:Person, let's say that you want each instance of my:Person to have a property my:hasFather with both (local) domain and range being my:Person. By "local", I mean that the range (and likewise the domain) is not a global feature of the property my:hasFather (something that you would express by an rdfs:range axiom), but it will only be inferrable for instances of class my:Person - the property my:hasFather may alternatively be used for things outside the class my:Person (such as animals), in which case the range of the property will be undetermined, unless specified elsewhere. You can get this behavior by the following subclass axioms:

(1)

# every my:Person is a foaf:Person
my:Person rdfs:subClassOf foaf:Person .

# every my:Person has exactly one father
# (not what you were asking for, but it makes some sense)
my:Person rdfs:subClassOf [
    owl:onProperty my:hasFather ;
    owl:cardinality "1"^^xsd:nonNegativeInteger ] .

# local range of my:hasFather: 
# the father of a my:Person is himself a my:Person
my:Person rdfs:subClassOf [
    owl:onProperty my:hasFather ;
    owl:allValuesFrom my:Person ] .

# local domain (what you were asking for!): 
# expressed by inverse property!
my:Person rdfs:subClassOf [
    owl:onProperty [ owl:inverseOf my:hasFather ] ;
    owl:allValuesFrom my:Person ] .

So, say you have within your data the triple

(2) my:alfred my:hasFather my:bob .

you will not immediately learn that my:alfred or my:bob are instances of my:Person. However, if you have the additional triple

(3a) my:alfred rdf:type my:Person .

then you will learn that my:bob is also a my:Person, as this is the local range of my:hasFather with regard to class my:Person. And, likewise, if you have the additional triple

(3b) my:bob rdf:type my:Person .

then you will learn that my:alfred is also a my:Person, as this is the local domain of my:hasFather with regard to class my:Person.

Things you should avoid:

• Although quite obvious, it should be stated anyways: Do not make class foaf:Person a subclass of any of the given restriction class expressions (neither the owl:cardinality nor the owl:allValuesFrom expressions), as this would change the intended meaning of class foaf:Person: Suddenly, every foaf:Person will have some my:hasFather relationship!

• Less obvious: Also do not make those restriction class expressions subclasses of foaf:Person, with the idea to have them "in the middle" between foaf:Person and my:Person, as this would have the semantic side effect that every individual that can be inferred to have either exactly one or zero(!) properties my:hasFather will become a foaf:Person.