Regarding: Jaenisch - Schumov Casual Series (1850)

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<Die beiden nachfolgenden Partieen hat Herr von Jänisch neuerdings mit Herrn Schumoff gespielt. Der Letztere, noch vor einigen Jahren ein Schüler unseres genialen Freundes, beginnt jetzt schon mit demselben un die Palme zu streiten, und legt, namentlich in der Partie 244, ein grosses Talent an den Tag. Die Anmerkungen zu diesen Partieen rühren zum grösseren Theile von Herrn von Jänisch her.>
Source: Schachzeitung, v5, January 1850, p37

243. C Jaenisch vs Shumov, 1849 (44 move B20 Sicilian)
244. C Jaenisch vs Shumov, 1849 (28 move B20 Sicilian)

Note: Two additional games are given as Games 251 (page 174) and 252 (page 175) in the May 1850 index but that issue is missing in the available online volume, however the Oxford Encyclopedia of Chess Games gives four games and cites Schachzeiting 1850 as the source for all four. The two additional games are:

Shumov vs C Jaenisch, 1850 (20 move C44 King's Pawn Game)
Shumov vs C Jaenisch, 1850 (19 move C53 Giuoco Piano)

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<The following games between the well-known author on Chess, Major C. F. de Jaenisch and another amateur of St. Petersburgh, have been kindly forwarded to us by the former for publication.>
Source: Illustrated London News, 1850.06.29, p459

Shumov vs C Jaenisch, 1850 (48 move C41 Philidor Defense)
Shumov vs C Jaenisch, 1850 (20 move C44 King's Pawn Game)

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<The following games were played at St. Petersburgh, between Major C. F. de Jaenisch and Mr. Schumoff.>
Source: Chess Player's Chronicle, v11 n7, July 1850, p193

Shumov vs C Jaenisch, 1850 (48 move C41 Philidor Defense)
C Jaenisch vs Shumov, 1849 (44 move B20 Sicilian)

<Of the opening in this game, Major Jaenisch remarks that "it seems to require a more satisfactory analysis. The greatest English authority pronounces in favour of the attack (see the Chess Player's Handbook, p. 151), the greatest German authority (see the Berliner Schachzeitung 1848, p. 79) hold a contrary opinion. In the hope to decide the question Messrs Jaenisch and Schumoff have commenced a series of games at this opening, of which the following is one. It will at least serve to illustrated the dangers to which the open position of the Black King exposes him if the least error be made in the defence.">
Source: Chess Player's Chronicle, v11 n7, July 1850, p196

Shumov vs C Jaenisch, 1850 (20 move C44 King's Pawn Game)
Shumov vs C Jaenisch, 1850 (19 move C53 Giuoco Piano)

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Conclusions:

Based on the publication dates, I suspect these two games were probably played around December 1849:
C Jaenisch vs Shumov, 1849 (44 move B20 Sicilian)
C Jaenisch vs Shumov, 1849 (28 move B20 Sicilian)

With the following three games being played around April 1850:
Shumov vs C Jaenisch, 1850 (20 move C44 King's Pawn Game)
Shumov vs C Jaenisch, 1850 (19 move C53 Giuoco Piano)
Shumov vs C Jaenisch, 1850 (48 move C41 Philidor Defense)

With the Scotch game (20 move C44 King's Pawn Game) being part of a series of games played to test Scotch Game opening theory based on the statement published in the Chess Player's Chronicle. None of these games appears to have been played in any type of formal match, and only one games appears to come from theoretical series. The others would appear to be offhand, i.e. casual, games.

Jaenisch - Schumov casual games 1849:
https://www.chessgames.com/perl/che...

Jaenisch - Schumov casual games 1850:
https://www.chessgames.com/perl/che...

Jaenisch - Schumov casual series of Scotch games 1850:
Jaenisch - Schumov Casual Series (1850)