How do I adjust an expense that was received and paid in April, but it refers to expenses in January? The period for January is already closed.

Technically you should have a prior period adjustment where you would debit retained earnings instead of the expense account in April. However, if your financial reporting period fell between January and April then you would have to restate your financial statements and this could be costly and time consuming. If you did produce your F/S and the item is immaterial then don't worry about it and just leave it in April. If you did not produce F/S then you have no problem and you can debit retained earnings instead of the expense account. Hope this helps