NEW YORK — Chesapeake Energy Corp.’s bid to tap new sources of natural gas in New York State may be quashed by Gov. David A. Paterson’s political troubles.

Paterson is the most prominent state proponent of drilling in the Marcellus Shale, a formation extending from West Virginia to New York that has helped spur a boom in U. S. shale-gas production. Chesapeake, the second-biggest producer of natural gas in the United States, is one of three companies that have filed a combined 58 applications for drilling permits in the state.

Paterson’s Department of Environmental Conservation is completing rules for extracting the gas. Applicants had expected permits to be approved this year, said Dave Palmerton, an industry consultant. That was before the governor became the target of probes into allegations that he improperly contacted a woman who had accused an aide of domestic abuse and that he sought free tickets to baseball’s World Series.

“Up until recently, he was in a position to push Marcellus drilling in New York State,” said Palmerton, who is based in Syracuse. “Given the political pressures right now, I’m very concerned the DEC may be pressed to hold this up until after the election, or delay it for some indefinite period of time.”

Oklahoma-based Chesapeake, Calgary-based Talisman Energy Inc. and privately held Vertical Resources Inc., based in Sugar Grove, Pa., all want to drill in New York. More companies would follow, said Vertical President Steve Ford.

Chesapeake dropped plans last year to drill in the part of the Marcellus Shale that lies beneath the New York City watershed after environmentalists and city officials said drilling would contaminate the water supply.

Jim Gipson, a Chesapeake spokesman, said it was a business decision not to drill in the city watershed. In an October statement, Chesapeake said it was “the most active driller” in the formation and expected to be the largest producer of gas from it.

Since 2007, discoveries of unconventional gas, including that taken from shale, have more than doubled the estimate of North American reserves to 3,000 trillion cubic feet, enough to meet 100 years of demand, according to energy consultants. The Marcellus Shale alone may contain 50 trillion cubic feet of gas.

Buffalo-based National Fuel Gas Co. also has big plans to increase drilling in the Marcellus Shale in Pennsylvania, where it owns vast drilling rights, but it does not currently drill in the New York State portion of the Marcellus formation.

Gas production for National Fuel Gas grew by 21 percent in the final three months of 2009 due to strong results from its first three Marcellus wells. The company hiked its production forecast for the current fiscal year to the equivalent of 44 million and 51 million barrels of oil, up from its previous projection of 42.5 million and 50 million barrels.

David F. Smith, National Fuel’s new chairman and CEO, has said he wants to increase drilling in the region.

Paterson wants to tax shale gas and has anticipated revenue starting in the fiscal year that begins April 1, 2011, according to his budget proposal. The State Senate has proposed dropping the tax.

Drilling 300 wells would generate $1.4 billion annually, including $100 million in lease payments to landowners and $32 million in tax revenue, according to the Independent Oil & Gas Association of New York.