Transition-metal-catalyzed carbene-involved cross-coupling reactions have meet substantial achievements in pursuit of efficient and practical synthetic strategies to construct carbon-carbon bonds. N-tosylhydrazones derived ketones or aldehydes have emerged as reliable carbene precursors in the coupling reactions through a sequence of in situ generation of diazo compounds, metal carbene formation and migratory insertion. Chirality introduction, hence, is anticipated to achieve on the metal carbene species in the employment of chiral ligands since a more preferred orientation for the migratory insertion can determine the corresponding central chirality on the ipso carbon center. Such stereoenriched metal species, whether through a protonation step or captured by the indicated nucleophiles, will furnish the corresponding chiral C-C coupling products. In this field, copper-catalyzed asymmetric synthesis of trisubstituted allenes (or alkynes) has been achieved in the coupling of diazoalkanes (or hydrazones) with terminal alkynes where the protonation process closures the reaction (Scheme 1a, top). Besides, terminal alkynes and silylboronic esters as nucleophiles are envisaged to terminate the catalytic cycle, thus two carbon-carbon bonds can be constructed in an enantioselective three-component reaction manner (Scheme 1a, bottom). In addition, the aforementioned stereoenriched metal species also demonstrated its utility in the assembly of axial and inherent chirality whether through a β-H or β-heteroatom elimination pathway. Synthesis of axially chiral vinyl arenes in the reactions of hydrazones and aryl bromides was pioneered in 2016, in which the tetrahydronaphthalene moieties could guarantee the essential β-H elimination and emergence of diaryl phosphine oxide substituted atropisomers (Scheme 1b, top). In a comparable method, an elegant work in the assembly of axially chiral cyclohexylidenes was reported via a β-OH elimination process in the aryl coupling reactions whereas for diazo substrates restricted to the cis conformation (Scheme 1b, middle). As a comparison, benzyl bromides were tolerated in the carbene coupling reactions as well in which still the process of β-H elimination facilitated the formation of inherently chiral seven-membered rings (Scheme 1b, bottom). Enantioenriched cyclobutanes are considered as valuable moieties in biologically active molecules and chemical synthesis. Owing to the inherent rigid structure and strainrelease driven ring decomposing interference, the synthesis of such susceptible molecules still poses certain challenges in an asymmetric catalytic way. Axially chiral alkylidenecyclobutanes as one representative type of such enantioenriched fourmembered rings, the corresponding synthetic strategy remains elusive. Asymmetric allylic substitution reactions have exhibited recognized versatility in the assembly of stereocenters on the strained rings, and they were proven of reliability when utilizing the tailed 1-vinyl substituted cyclobutyl acetates to obtain axially chiral alkylidenecyclobutanes accordingly. In this content, one report is a palladium-catalyzed asymmetric allylic alkylation reaction of 1-vinylcyclobutyl acetates disclosed in 2022, and the other arose as a comparable asymmetric hydrogenolysis strategy very recently, both leading to the access of enantioenriched alkylidenecyclobutanes (Scheme 1c, X = OAc). Furthermore, 1vinylcyclobutyl substrates bearing the free hydroxyl group could deliver the chiral alkylidenecyclobutanes as well enabled by the copper-catalyzed borylation reaction in a desymmetric fashion (Scheme 1c, X = OH). These three representative works involving the allylation chemistry have addressed the obstacle of synthesizing axially chiral alkylidenecyclobutanes, whereas thorough issues remain critically in terms of the envisaged compatibility of forging such axial chirality with four-membered ring retention on the basis of carbene chemistry. Our group once reported a carbene coupling reaction of cyclobutanone-derived hydrazones with benzyl halides enabled by palladium catalysis, aimed to construct axial chirality on the fourmembered rings though encountered low enantioselectivities. The point at issue is how to tame the strained carbene coupling reactivity in an enantioselective and stereospecific manner, through a thorough consideration of the susceptibility of strain-released driven ring opening and hyperactive strained carbene initiated ring expansion. Following our continuous interests in the field of three-and four-membered rings, especially for the asymmetric transformations, we herein disclosed a palladium-catalyzed phosphoramidites L4, L5，and R-BI-DIME L6, and the results revealed that none of them exhibited decent reactivities or enantioselectivities except for a moderate ee value when using L4. Considering its versatility of Sadphos in the palladium-catalyzed asymmetric coupling reactions, we then turned to investigate this type of chiral ligand, including ditert-butylphosphine derived TY-Phos, diadamantylphosphine derived Xiao-Phos, dicyclohexylphosphine derived Xu-Phos, and diphenylphosphine derived Ming-Phos. The application of Xu-Phos L9 and Ming-Phos L12 delivered the corresponding product 3a in both the recognized yields and enantioselectivities, 83% yield with 79% ee, and 95% yield with 81% ee respectively. Notably, N-methylated Xu-Phos L10 nearly shut down the reaction as trace amount of 3a was detected, indicating the essential of NH group in rendering the reactivity. The stereocenter inversed product ent-3a was more favored while utilizing Xu-Phos L11, the diastereomer of L9, albeit in both the distinctly dropped yield and enantioselectivity (38% yield with 60% ee). We afterwards focused on the modification of Xu-Phos and investigated their performance. The steric hinderance on the α-positioned phenyl ring of sulfinamide led to significant influence on the yields and enantioselectivities of 3a. In this context, ligand with the moiety of 3,5-di-tert-butyl-4-MeOC6H2 could slightly improve both the yield and enantioselectivity (92% yield with 85% ee) while the 3,5-di-Phenyl-4-MeOC6H2 one inhibited the enantioselectivity obviously though giving an excellent yield (96% yield with 77% ee). Bulkier substituent, the adamantly (Ad) group for instance, was introduced on the modified ligand L15, which was proven effective as 3a