Written (by Eddy Grant) and first recorded by The Equals (1967).
Hit album version by The Clash (1980).
From the wiki: “‘Police on My Back’ was written by Eddy Grant when he was leader of the Equals, a racially-mixed British group who fused rock, reggae, and soul rhythms. The band’s sole international hit was the admirably eccentric groover ‘Baby Come Back’. First released as a promotional single in Germany in 1967 and in 1968 in the UK, the Netherlands and Austria (with no apparent chart success), ‘Police on My Back’ was included on the Equals Explosion album released in the UK in 1968, and in the US in 1968 on the compilation ‘greatest hits’ album Baby, Come Back.
“The Clash picked ‘Police on My Back’ to cover while recording their fourth album, the sprawling three-LP set Sandanista!. While the Equals’ original version has a clear if muted reggae undertow, the song became a hard-charging, high-velocity onslaught when recorded by The Clash.
“‘Police on My Back’ was a rare example of the Clash tackling a reggae tune and, rather than trying to fuse its Caribbean rhythms with the band’s muscular approach, instead stripped the tune to its bare bones and tackling it as straight rock & roll. The track was cited by some critics in reviews of Sandinista! as the most ‘Clash-sounding’ song on the album – with the irony being that ‘Police on My Back’ was a cover; not a Clash original.”
The Clash, “Police on My Back” (1980):