Warner Amex Cable Communications has applied to Fairfax County for a 15-year franchise to operate the cable television system it has run in Reston since 1969, a move that would end a confrontation between the company and county officials and start a battle over who will serve the fast-growing area.

Warner Amex spokesman Wayne R. Hill said yesterday the company also would spend more than $2 million to upgrade the system so it would offer 51 standard channels instead of the current 21 or 27. The number of optional premium channels would expand from three to six.

Media General Cable of Fairfax, which has held a nonexclusive countywide franchise since 1982 and already serves 90,000 customers in other parts of the county, has a capacity of 120 channels, the largest of any in the country; Warner Amex's expansion would eventually give it a capacity of 78.

Warner Amex, with headquarters in New York, filed its franchise application Monday, barely meeting a Jan. 1 county deadline for any unlicensed operators to apply for legitimacy. The county Board of Supervisors must act on the application within six months.

If the supervisors approve, Reston residents could be in the enviable position of having two cable systems to choose from, at a time when residents of Montgomery County and the District still wait for cable hookup.

Media General officials, meanwhile, say they will go ahead with their plans to install cable in Reston.

The Warner Amex application would end a legal tussle with Fairfax County that began when the county filed suit against the cable firm for running an unlicensed operation. Company officials had argued they did not need a county franchise because they were operating under an agreement with Reston's developer.

Last spring, Warner Amex and the county agreed to drop their suits and countersuits over the issue in an effort to work things out. "There's no point in being at odds with a county government if you don't need to be," Hill said.

Warner Amex, in keeping with previously announced expansion plans, also applied to add 32 miles of cable lines to its existing 118 miles, enlarging its potential customer pool to 16,000 from the current 14,000, all in Reston. The firm now serves 9,000 households.

Warner Amex said that if its application is approved, it would cut prices in hopes of making up the revenue difference in volume business. It also would offer a 13-channel economy package for $3.95 a month.