We develop an universal method to significantly suppress probe-induced shifts in any types of atomic clocks using the Ramsey spectroscopy. Our approach is based on adaptation of the synthetic frequency concept [V. I. Yudin, et al., Phys. Rev. Lett. 107, 030801 (2011) At the present time, huge progress occurs for highprecision optical atomic clocks based on both neutral atoms in optical lattices [1][2][3][4][5][6][7][8] and trapped ions [9][10][11][12]. Exceptional accuracy and stability at the 10 −17 -10level are achieved. Potential possibilities to achieve the level of 10 −19 become clearer for nuclear clocks [13-16] and for highly charged ions [17][18][19]. Great fundamental (e.g., in tests of fundamental physical theories such as QED, QCD, unification theories, cosmology, dark matter searches, etc.) and practical (navigation and information systems, gravity-geopotential surveying) importance of the current and long-range researches is wellknown and unquestionable. Current state, concomitant problems, and future prospects are well presented in the review [20].On the way to these remarkable achievements, different barriers arise, which require the development of new unconventional approaches. As an example, for some of the promising clock systems, one of the key problems is the frequency shift of the clock transition due to the excitation pulses themselves. For the case of magnetically induced spectroscopy [21,22] these shifts (quadratic Zeeman and ac-Stark shifts) could ultimately limit the achievable performance. Moreover, for ultranarrow transitions (e.g., electric octupole [23] and twophoton transitions [24,25]) the ac-Stark shift can be so large in some cases to rule out high accuracy clock performance at all. A similar limitation exists for clocks based on direct frequency comb spectroscopy [26,27] due to ac-Stark shifts induced by large numbers of off-resonant * Electronic address: viyudin@mail.ru laser modes.Unconventional solution to this important problem was proposed in the paper [28], in which so-called hyperRamsey method has been developed. Soon this approach was successfully realized in [29], where the huge suppression (by four orders of magnitude) of probe-induced shifts was experimentally demonstrated (see also [9]). However, a potential of this method was not going to be settled. In the experimental-theoretical paper [30] a 'stunning' result was recently shown: certain simple modification allows, in principle, totally(!) to exclude probeinduced shifts. Other hyper-Ramsey modification, having the same efficiency, was very soon proposed in the theoretical paper [31]. Because these phenomenal results can have far-reaching consequences for development of atomic clocks, it requires utterly thorough investigation of the schemes [30,31]. Besides, undoubted importance has a search of new variants to suppress probe-induced shifts with the near extremal efficiency.In this paper, we develop an universal method to dramatically suppress probe-induced shifts and their fluctuations in any type of atomic clock...