In an effort to boost sagging passenger traffic, Trans World Airlines said yesterday it will slash promotional fares on most of its domestic routes by as much as 50 percent between April 20 and May 31.

Offering reductions of up to 70 percent from regular coach fares for the five-week period, the new "anywhere super saver" fare will enable TWA passengers to pay no more than $298 round trip for any of TWA's domestic routes, except Chicago-West Coast flights. Children up to 12 years will pay no more than $98 round trip on any of the flights.

As with most promotional fares, seats are limited and certain restrictions apply. TWA said the current super saver advance-purchase and minimum-stay requirements will apply. On most routes, this means passengers must buy tickets 14 days in advance and remain at the destination over a Friday night. Cross-country routes have a seven-day-advance-ticketing rule. Although trips using the discount fare must be started by May 31, passengers have up to 60 days to make the return trip.

As an example of the savings available with the special fare, TWA cited the current costs of flights between Washington, D.C., and Seattle. Currently, the regular coach fare is $716 round trip, and the round-trip super saver fares are $438 during the day, $394 at night and $322 for children. sThe round-trip "anywhere" fares will be $298 for adults and $98 for children.

It's very possible that other airlines will match TWA's reduced fares.

At a press conference in New York to announce the promotion, TWA officials said the new fares are designed to fill empty seats on TWA's planes, which have been flying about 54 percent full on the average this month. "With fares having risen the way they have, we've driven people from the marketplace," said Neil M. Effman, TWA's senior vice president of planning.