If the typosquatter is in another state or nation, then the fraud crosses state or international boundaries; hence, prosecuting the fraud against the typosquatter would be a federal matter of criminal fraud law.
Conversely, if the typosquatter is in Indiana, then there are two likelihoods: 1) Original-poster sys-admin might in fact be the typosquatter without any identity theft. OR 2) The typosquatter may be a fellow employee who seeks to gain in their own career by eliminating original-poster sys-admin from the company. Indeed, if it is #2 and if it were to turn out that the typosquatter is an officer of the employer's corporation, then the employer's corporation can be argued to have framed the employee. If the typosquatter-framer is a nonofficer that is, say, another sys-admin, then the employer is terminating the wrong employee as it stands right now, while retaining the guilty party in this hypothetical scenario.
Finding out whose credit card was utilized to purchase the domain name and whose credit card (or ACH identifiers to which the advertising revenue that is earned by the typosquatter domain is deposited) is the key to determining all future plans of attack on your defense. Regarding your employment per se, that is a matter of civil law. But the fraudulent use of your identity to frame you is a matter of either Indiana criminal code (if all parties are within Indiana) or United States federal code (if at least one party is outside of Indiana). If you, original poster, are innocent as you claim, then the typosquatter may be guilty of wire fraud in the use of typosquatter's credit card as a material part of typosquatter's commission of the fraud against you.
Think about it, you might be able to charge one of your fellow coworkers with criminal charges if they framed you to "help you find a new job". Once all of that dirty laundry is hung out on the clothesline, then the employer might see matters in an entirely different light. Your entire future hinges on ascertaining the credit-card billing info that was utilized to pay for the typosquatter domain and/or how payments are made regarding the advertising revenue earned by the typosquatter domain. Once you find out the billing info on credit cards or ACH info on other financial accounts and if any party (including the bank) is outside of Indiana, then go to the nearest FBI office and file a report of fraud. The main FBI office that serves Indiana is in Indianapolis, although there exist branches in several of Indiana's larger cities too.
To get this credit-card billing info, you should hire a lawyer on a pay-by-the-hour basis, without retainer fee beyond having a credit card on file and perhaps prepaying the first 2 hours or so and a contract that doesn't have too many terms beyond: original poster promises to pay for the billable-hours incurred. Lawyers with sizable retainer fees (and lengthy retainer contracts) are usually pursuant to litigation against an adversary, but litigation against a known adversary is not what you want right now. You need to find your adversary (the typosquatter), then convince a government prosecutor to pursue the litigation against the typosquatter, if the typosquatter is within the USA. You want to convert this purely civil matter into a criminal matter ASAP. Hourly lawyers that do not require multithousand-dollar retainer fees up front are the kind of lawyer that you need: filing the magical paperwork to get accomplished the things that you need right now, such as subpeonaing the typosquatter's financial information from the domain registrar or from the hosting service at which the typosquatter domain is parked. Still, you are going to spend at least a four-digit sum for the no-retainer lawyer to file the magical paperwork for you. You can save money by being the investigator yourself, doing all the leg-work; you would delegate only the filing of legal paperwork in courts to the lawyer (instead of utilizing the lawyer as an expensive private investigator of sorts). Most importantly, this lawyer is your attack dog against the typosquatter. This lawyer would hardly know that your employer exists. This lawyer would most likely be a criminal lawyer or a contract-law lawyer or both, not an employment-law lawyer (because you need to go after the typosquatter, not your employer). Somehow showing the employer your criminal-investigation good works comes later, perhaps with the aid an employment lawyer.