Family Matters
Family Matters is an American sitcom which originated on ABC from September 22, 1989 to May 9, 1997, before moving to CBS from September 19, 1997 to July 17, 1998.
 A spin-off of "Perfect Strangers," the series revolves around the Winslow family, a middle-class African American family living in Chicago, Illinois.
 Midway through the first season, the show introduced the Winslows' nerdy neighbor Steve Urkel (Jaleel White), who quickly became its breakout character and eventually the show's main character.
 Having run for nine seasons, "Family Matters" became the second longest-running non-animated US sitcom with a predominantly African American cast, behind only "The Jeffersons" (11).
 Having aired 215 episodes, "Family Matters" is ranked third, behind only "Tyler Perry's House of Payne" (254), and "The Jeffersons" (253).
Jesse Frederick
Jesse Frederick James Conaway (born 1948), known professionally as Jesse Frederick, is an American film and television composer and singer best known for writing and performing the themes to TGIF television shows such as "Perfect Strangers", "Full House", "Family Matters", and "Step By Step" for ABC.
Freddie Perren
Frederick James "Freddie" Perren (May 15, 1943 – December 16, 2004) was an American songwriter, record producer, arranger, and orchestra conductor best known as co-songwriter and co-producer of such mega-hits as "Boogie Fever" by the Sylvers, "I Will Survive" by Gloria Gaynor, and "Shake Your Groove Thing" by Peaches & Herb.
Denise Huxtable
Denise Huxtable Kendall is a fictional character who appears on the American sitcom "The Cosby Show" (1984 – 1991), portrayed by actress Lisa Bonet.
 Denise also stars in the first season of its spin-off sitcom, "A Different World" (1987).
 The second-born child of Cliff and Clair Huxtable, Denise is known for her eccentric clothing and free-spirited, rebellious nature, earning her a reputation as the Huxtable family's "wild child".
 Alternating between regular and recurring character, Denise appears on-and-off throughout the sitcom's eight-year run, from its pilot "Theo's Economic Lesson" to the seventh season episode "Cliff and Jake", for a total of 98 episodes, after which Bonet departed for the remainder of the series.
Good News (TV series)
Good News (also known as The Good News) is an American sitcom and a spin-off of "Sparks" that aired on UPN from August 25, 1997 to May 19, 1998.
 It is also the final TV series to be produced by MTM Enterprises, before it was folded into 20th Century Fox Television.
Rhoda
Rhoda was an American sitcom starring Valerie Harper which aired a total of 109 half-hour episodes and one hour-long episode over five seasons from September 9, 1974 to December 9, 1978.
 The show was a spin-off of "The Mary Tyler Moore Show", in which Harper between the years 1970 and 1974 had played the role of Rhoda Morgenstern, a spunky, weight-conscious, flamboyantly fashioned Jewish neighbor and native New Yorker in the role of Mary Richards' best friend.
 After four seasons, Rhoda left Minneapolis and returned to her original hometown of New York City.
 The series was the winner of two Golden Globes and two Emmy Awards.
Jesse Armstrong
Jesse Armstrong is a British comedy writer, best known for the Channel 4 sitcom "Peep Show" and the BBC political satire "The Thick of It".
 He is from Oswestry in Shropshire, and attended a comprehensive school there before reading American Studies at the University of Manchester, where he met his writing partner Sam Bain.
 Before going into comedy writing in the late 1990s, Armstrong worked as a researcher for the Labour MP Doug Henderson.
I'll Be There for You (The Rembrandts song)
"I'll Be There for You" is a song recorded by the American duo The Rembrandts.
 It is best known as the theme song to the American sitcom "Friends", which premiered during 1994 and ended in 2004.
 The song was also released as the first single from the group's third studio album "LP".
Yoko Takahashi
Yōko Takahashi (高橋 洋子 , "Takahashi Yōko" , born August 28, 1966) is a Japanese singer from Tokyo, best known for performing "A Cruel Angel's Thesis" (残酷な天使のテーゼ , "Zankoku na Tenshi no Tēze" ) , the opening theme song of the anime series "Neon Genesis Evangelion".
 She also performs the closing theme, an "acid bossa" version of "Fly Me to the Moon" and "Tamashii no Rufuran" (魂のルフラン , Tamashii no Rufuran , "Refrain of Soul") , the closing theme of "".
 She also performed "Metamorphose," the opening theme to studio Gainax's 20th anniversary series, "This Ugly Yet Beautiful World," the ending theme "Yoake Umarekuru Shōjo" (夜明け生まれ来る少女 , "The Girl who was Born at Dawn" ) for the anime "Shakugan no Shana" (灼眼のシャナ , "Blazing-Eyed Shana" ) and the opening theme "Aoki Flamme" for "Pumpkin Scissors" (パンプキン・シザーズ , "Panpukin Shizāzu" )
Glenn Quinn
Glenn Martin Christopher Francis Quinn (May 28, 1970 – December 3, 2002) was an Irish actor in television and film, known for playing Mark Healy in the American sitcom "Roseanne", and Doyle, a half-demon, on "Angel", a spin-off series of "Buffy the Vampire Slayer".

Question:  Jesse Frederick James Conaway is best known for writing and performing the theme to an American sitcom that was a spin-off of what series? 
Answer: Perfect Strangers