It depends how you define “conjunction.” For example, this year, Jupiter and Saturn will be at the same ecliptic longitude and the same right ascension within hours of each other on December 21, 2020. However, in 2000, they were at the same right ascension on May 30, but at the same ecliptic longitude on May 28, 2000.
I have done calculations (using the VSOP87 planetary theory for positions and Meeus’ Astronomical Algorithms, Second Edition, 1998, for dates of solstices), for conjunctions measured by ecliptic longitude. The result is at https://astronomie.quebec/conjsols.html
This doesn’t give you the precise moment of conjunction; it just lists solstices where Jupiter and Saturn were at less than 5° from each other, between the years −1000 and +3000. As you can see for 2020, the spacing between the two in ecliptic longitude (i.e. neglecting latitude difference) is 0.0387°. The last time these planets were so close in ecliptic longitude at the solstice was in −204 (i.e. 205 BCE).
The only other times in the time span calculated where Jupiter and Saturn were at less than 0.1° in ecliptic longitude (again, neglecting latitude) at the solstice are in −860 and in +2159.
Interestingly, it is in 2020 that the planets are so close in latitude as well at the solstice; their spacing was slightly more that 56′ in 861 BCE and slightly more than 19′ in 205 BCE; and will be more than 1° 12′ in 2159 CE. (Again, these are spacings at the solstices; they may come closer at other dates than solstices, but your question was solstices.)
