If you find one you want to hire, ask about his track record, what fees and costs he would charge, etc. Know as much as you can before this gets to a courtroom.
But it's also a good idea to inquire on your own to the agency that is pursuing you. Ask them what evidence they have that you are the parent. Do they have a driver's license number, an SSN, license plate, an address of residence? Ask what other names this women may have had. What is her age, weight, hair color, race, etc? Do they have a photo they could fax? Do NOT ask for an address or phone number of the woman as you don't want to hint that you might respond with any threats or violence. You just want information that would help you recall any encounter at all with this person.
If they provide you with details, you can then go about gathering evidence that this person they are looking for cannot be you (bill statements of the time frame in question, tax returns, other official proof of residence). Agree to mail or fax to them any information you think will clear this up but *do not* send any original documents.
Then, if they don't back off, that's when you hire the lawyer and prepare to fight. Be prepared to submit to DNA testing.
And remember, when you are asking how much you can afford for a lawyer, keep in mind how much the family courts could award this woman for the next 13 years to take care of two kids you don't know. His services could be worth a lot of money you *don't* have to pay out.