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(1) Introduction: The subject of the present study concerns the analysis of the existence and long time evolution of the solar ~200 yr (de Vries/Suess) and ~2400 yr (Hallstadt) cycles during the recent part of the Wurm ice epoch and the Holocene, as well as their forcing on the regional East European climate during the last two calendar millennia. The results obtained here are compared with those from our previous studies, as well as with the results obtained by other authors and with other types of data. A possible scenario of solar activity changes during the 21st century, as well as different possible mechanisms of solar–climatic relationships, is discussed. (2) Data and methods: Two types of indirect (historical) data series for solar activity were used: (a) the international radiocarbon tree ring series (INTCAL13) for the last 13,900 years; (b) the Schove series of the calendar years of minima and maxima and the magnitudes of 156 quasi 11 yr sunspot Schwabe–Wolf cycles since 296 AD and up to the sunspot cycle with number 24 (SC24) in the Zurich series; (c) manuscript messages about extreme meteorological and climatic events (Danube and Black Sea near-coast water freezing), extreme summer droughts, etc., in Bulgaria and adjacent territories since 296 and up to 1899 AD, when the Bulgarian meteorological dataset was started. A time series analysis and χ2-test were used. (3) Results and analysis: The amplitude modulation of the 200 yr solar cycle by the 2400 yr (Hallstadt) cycle was confirmed. Two groups of extremely cold winters (ECWs) during the last ~1700 years were established. Both groups without exclusion are concentrated near 11 yr sunspot cycle extremes. The number of ECWs near sunspot cycle minima is about 2 times greater than that of ECWs near sunspot cycle maxima. This result is in agreement with our earlier studies for the instrumental epoch since 1899 AD. The driest "spring-summer-early autumn" seasons in Bulgaria and adjacent territories occur near the initial and middle phases of the grand solar minima of the Oort–Dalton type, which relate to the downward phases and minima of the 200 yr Suess cycle. (4) Discussion: The above results confirm the effect of the Sun's forcing on climate. However, it cannot be explained by the standard hypothesis for total solar irradiation (TSI) variations. That is why another hypothesis is suggested by the author. The mechanism considered by Svensmark for galactic cosmic ray (GCR) forcing on aerosol nuclei was taken into account. However, in the hypothesis suggested here, the forcing of solar X-ray flux changes (including solar flares) on the low ionosphere (the D-layer) and following interactions with the Earth's lithosphere due to the terrestrial electric current systems play a key role for aerosol nuclei and cloud generation and dynamics during sunspot maxima epochs. The GCR flux maximum absorption layer at heights of 35–40 km replaces the ionosphere D-layer role during the sunspot minima epochs. [ABSTRACT FROM AUTHOR]