`Epilog` puts graphics primitives after the plot is drawn. The legend has to be put together manually.

 Plot[x^2, {x, 0, 2}
 , Frame -> True
 , ImageSize -> 400
 , Epilog -> {AbsolutePointSize[6], Red, Point@{1, 1}}
 , PlotLegends -> Placed[
 LineLegend[{Blue, Red}
 , {"\!\(\*SuperscriptBox[\(x\), \(2\)]\)", "Red dot"}
 , LegendLayout -> {"Column", 1}
 , LegendFunction -> (Framed[
 #, Background -> GrayLevel[0.9]
 , RoundingRadius -> 4
 ] &)
 , LegendMarkers -> {""
 (*Graphics[{AbsoluteThickness[5]
 ,Line[{{-0.5,0},{0.5,0}}]}]*)
 , Graphics[Disk[]]}]
 , {1, 0.5}
 ]
 ]

[![enter image description here][1]][1]

For the specific case mentioned in the OP:

 Plot[x^2, {x, 0, 2}
 , Frame -> True
 , ImageSize -> 400
 , Epilog -> {AbsolutePointSize[6], Red, Point@{1, 1}}
 , PlotLegends -> Placed[
 LineLegend[{Blue, White}
 , {"\!\(\*SuperscriptBox[\(x\), \(2\)]\)", "Red dot"}
 , LegendLayout -> {"Column", 1}
 , LegendMarkers -> {""
 , Graphics[{Red, Disk[]}]}]
 , {1, 0.5}
 ]
 ]


 [1]: https://i.sstatic.net/1vwSr.png