In 1871 I think John and Ellen's surname is transcribed as Rogus and they are living at Wallsend
Living with them and listed as a son is Alexander Rogers age 11 born Neston Cheshire. Presumably born prior to John and Ellen's marriage and therefore most probably born Alexander Jeffrey and named after Ellen's father
Found an Alexander Jaffrey age 1 born Cheshire in 1861 living as nephew with the following family in Roberts Row, Saltney, Great Boughton, Cheshire. Their surname is transcribed as Muller but looks more like Miller.
Agnes Muller Wife Married 30 Blacksmiths Wife Scotland
John Muller11 Scotland
Robert Muller 9 Scotland
Agnes Muller 3 Scotland
Ellen Muller1 Chester, Cheshire, England
Alexander Jaffery Nephew 1 Chester, Cheshire, England
William Cray Lodger 23 Plumber Scotland
John Gallacher Lodger 26 Blacksmiths Labourer Ireland
Kay
Edit - There is a birth of an Alexander Rogers in Jun Qtr 1860 Wirral 8a 408