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Is it not possible that foreign key(single column) in a child table references to a parent key which has some duplicate values?
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A foreign key can refer to either a unique or a primary key of the parent table. If the foreign key refers to a non-primary unique key, you must specify the column names of the key explicitly.
Creating a foreign key is almost as easy as creating a primary key, except that SQL Server imposes several more rules on foreign keys. For example, the foreign key must reference a primary key or unique constraint, although that reference can be on the same table or on a different table.
A table can have multiple foreign keys based on the requirement.
By the SQL standard, a foreign key must reference either the primary key or a unique key of the parent table. If the primary key has multiple columns, the foreign key must have the same number and order of columns. Therefore the foreign key references a unique row in the parent table; there can be no duplicates.
Re your comment:
If T.A is a primary key, then no you can't have any duplicates. Any primary key must be unique and non-null. Therefore if the child table has a foreign key referencing the parent's primary key, it must match a non-null, unique value, and therefore references exactly one row in the parent table. In this case you can't make a child row that references multiple parent rows.
You can create a child row whose foreign key column is NULL, in which case it references no row in the parent table.
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