At present, Standard Model （SM） is the most successful theory to explain the com-position and interaction of the matter, and Quantum Chromo Dynamics （QCD） is the elementary theory of strong interaction in the framework of SM. The predictions of the QCD in the high energy regime have been extensively approved. However, QCD be-comes invalid in the low energy regime due to the perturbative theory does not work in the case of the large effective coupling. Therefore, it is more important to study the hadron physics experimentally in the low energy regime, which is one of the main rea-sons that the Beijing Electron-Positron Collider （BEPCⅡ） operates at the center of-mass energy within 2.0 -4.6 GeV. According to the current knowledge, a meson consists of quark and anti-quark pair, and a baryon consists of three quarks. In addition, QCD also predicts the existence of the exotic states, such as the glueball, hybrid, multi-quark and molecule states and so on. The Beijing Spectrometer （BESⅢ） is not only a gen-eral purpose magnetic spectrometer operating at BEPCII, but also a worldwide unique detector running at the energy region of 2.0 - 4.6 GeV. Since successfully constructed in 2008, BESⅢ has accumulated the largest samples of J/ψ and ψ（2S） in the world.The decays of J/ψ and ψ（2S） can provide not only the unprecedented opportunity for studying the hadron spectroscopy, but also the excellent laboratory for searching the exotic states and new physics beyond the SM. In 2003, a strong enhancement near the pp mass threshold, known as the X（pp）, was first observed by the BESⅡ experiment in the radiative decay J/ψ→γpp. It was later confirmed by the CLEO and BESⅢexperiments. In theory, X（pp） is assumed to be a baryonium, a multi-quark state or an effect due to pure final-state interaction （FSI）, its nature has not been clarified yet. In addition, long time ago it was proposed that pΦ production is well suited to search the exotic pentaquark candidate with hidden strangeness. Just in 2015, LHCb reported the observation of two charmonium pentaquark structures with the quark content ccuud in the pJ/ψ mass spectrum. Therefore, it is very important to search the pentaquark candidate with the quark content ssuud in the pΦ or pΦ mass spectrum.Using the data sample of 4.48×108 ψ（2S） events accumulated with the BESⅢdetector, the decay ψ（2S） → ppΦ is studied in detail via two decay modes Φ →K+K- and Φ→KSOKLO. The average branching fraction of ψ（2S） → ppΦ is measured to be B（ψ（2S）→ppΦ） = （6.33 ± 0.36（stat） ± 0.43（syst）） x 10-6 for the first time and the result has verified 12% rule very well. No significant enhancement near pp invariant mass threshold is observed and the upper limit on the branching fraction of B（ψ（2S）→X（pp）Φ）.B（X（pp）→pp） is measured to be 1.92 x 10-7at90%confidence level （C.L.）. The mass spectrum of pΦ and pΦ are also studied but the evidence of the resonance BΦ is not prominent.In addition, at the present level of sensitivity, N - N oscillations probe intermedi-ate energy scales, between the Electro weak and Grand unification theory scale. N - N oscillations have been performed in the past, both with free neutron beams and within nuclear environment in large underground detectors. The best limit on the characteristic time of oscillation derived from free neutron beam is τN-N > 0.86 × 108s from Insti-tute Max von Lau-Paul Langevin （ILL） experiment at Grenoble, France. If N - N oscil-lation exits, then （Λ-Λ）oscillation may also take place, as firstly proposed by K.B.Luk,and the possibility of searching for theΛ-ΛA oscillations for coherent ΛΛ produc-tion, using quantum correlation to extract the oscillation parameters, in the J/ψ→ΛΛdecay process was firstly proposed by Xian-Wei Kang and Hai-Bo Li. Assuming no signal events for J/ψ) → ΛΛ the estimated upper limit on R < 3.5 x 10-7 with one year’s luminosity at BES-Ⅲ. In this thesis, a search for J/ψ →ΛΛ+ charge conju-gation （c.c.） is carried out with huge data sample accumulated at the center-of-mass energy （?）=3.097 GeV with the BESIII detector at BEPCII collider, corresponding to 1310.6 million J/ψ events. J/ψ →ΛΛ channel is also studied to check the consistency of results and also for normalization to avoid some sources of systematic uncertainities.The branching fraction value achieved for J/ψ→ΛΛ is consistent with BESⅢ al-ready published value within statistical systematic uncertainty. The upper limit on the ratio of two oscillation possibilities is determined to be 5.95 x 10-6, which is slightly one order above the predicted value proposed by Xian-Wei Kang and Hai-Bo Li due to lower statistics.