Nassau lawmakers voted to slash a proposed $105 fee on traffic tickets nearly in half Monday and eliminate the surcharge on parking tickets — setting the stage for a showdown with the county’s fiscal control board, which says the cuts create a $36 million hole in the 2017 proposed county budget.

GOP legislators plan to fill the shortfall with revenue from a “partial amnesty” program allowing businesses that have not complied with a 2013 county law requiring them to timely report their finances to pay 75 percent of their accrued fines.

The Nassau Interim Finance Authority has vowed to reject the budget if it relied on revenue from the income and expense law, which is being challenged in court, and impose its own changes.

Majority Republicans on Monday approved a series of amendments to the county’s $2.9 billion budget, which it passed last month, including roughly $40 million in new fees.

The most controversial item — a $105 “public safety fee” on traffic and parking tickets to pay for 150 new police officers and 81 civilian law enforcement employees — was reduced in scope. Motorists will now pay a $55 fee for all traffic violations, including red-light camera tickets, but would not pay an added surcharge on parking tickets.

The measure passed 11-8 with Legis. Denise Ford (R-Long Beach) voting with Democrats against the fee.

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“We need to find actual solutions, actual revenue that can pass NIFA muster,” said Legis. Steven Rhoades (R-Bellmore).

Minority Leader Kevan Abrahams (D-Freeport) called the public safety fee “an illegal motorist tax” that is “driving families out of Nassau.”

Republicans contend the amnesty program, which was approved by lawmakers in a party-line vote Monday, will generate at least $36 million — enough to fill the hole left by cutting the public safety fee. The independent Office of Legislative Budget Review said businesses who have not complied with the law owe an estimated $70.4 million.

A challenge to the income and expense law is expected to be heard by the Appellate Division of the State Supreme Court next year.

In a letter to lawmakers last week, NIFA Chairman Adam Barsky said the board was prepared to reject the budget when it meets Nov. 29 and send it back to the legislature for changes, arguing that revenue from the amnesty program “was unlikely to be realized.”

Without additional cuts, Barsky said NIFA would “impose a budget that removes at least $36 million” in spending.

Eric Naughton, Nassau’s deputy county executive for finance, provided NIFA on Monday with a list of $36 million in proposed cuts if NIFA rejects the budget.

The “contingency plan” calls for delaying $25 million in payments from the operating budget to pay for tax refunds; eliminating $4.1 million in funding youth service programs and $3.8 million for Nassau’s bus service and cutting $1.6 million from community policing programs.

Naughton said the cuts “will be painful and cause disruption” but will allow the county to “maintain essential services and prevents the layoffs of county employees.”

Jeffrey Reynolds, president and CEO of the nonprofit Family and Children’s Association in Mineola, said the cuts to youth programs will exacerbate the county’s heroin epidemic.

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“Cutting these services virtually guarantees that 2017 will mean even more fatalities,” Reynolds said.

Lawmakers Monday also approved $11 million in new business registration and Parks Department fees.

For example, fitness clubs and pet groomers would need to pay $600 for a county license while firms offering tax assessment reduction services would pay Nassau $1,000.

Also Monday, Arnold Drucker was sworn in as legislator in the 16th District. Drucker, who won the seat in a special election on Nov. 8, replaces the late Judy Jacobs.